ShowKase & GoDaddy

I'm sorry to hear that you're having trouble with Showkase.
I hope my notes below help.

First of all, please let me try to reassure you that installing and using Showkase should be a quick, easy and error-free process.
I have free web hosting accounts with three different web hosts that I use for occasional personal use and Showkase runs fine out-of-the-box on all three (AwardSpace, ByetHost and x10Hosting).
I won't go out of my way to recommend any of the web hosts that I use as they are free accounts with limited features and no priority support. Having said that, Showakse runs on all of them without issue.
The System Requirements noted here are really all that should be necessary.

Your problem certainly seems to stem from GoDaddy's migration of your site.

Normally, after migrating a site, you'd need to run Setup ('System -> Setup' from the Showkase admin) to let Showkase know the new location of the site.
Also, if a site fails, then I'd also recommend trying 'System -> Repairs -> Repair' (to rebuild the page records).
Finally, if the above two suggestions fail, I'd suggest installing a fresh Showkase site (in a separate directory so that it does not interfere with your existing site) to see if this works (and if it does, then you could import the pages from your existing site via 'Site -> Import' to avoid having to recreate them all from scratch).
Incidentally, it is still worth making a complete backup of your dysfunctional site just now so that you can import pages from it into a new site at some point in the future.

However, the File Test failures that you posted (from the Server Compatibility Test) suggest that nothing I've mentioned above is likely to work and that the problem is an incorrectly configured server.

The first File Test is simply trying to create a new directory on the server.
If GoDaddy's support cannot figure out why a PHP script is unable to create a new directory, then I'm really not sure what to suggest. That's pretty much as basic as a file management task can be.
The fact that you mentioned "GoDaddy no longer supports html coding" is especially worrying!

I think the clue is in the word 'Plesk' (in the File Test paths).
As far as I am aware, GoDaddy uses Plesk for its Windows servers and I've seen issues with GoDaddy/Plesk/Windows in the past.
I wonder if GoDaddy would be willing to move you over to a Linux server (being that their migration has broken your site and they can't fix it)?
I have a hunch (it's a strong hunch, not just a long-shot) that running Showkase on a GoDaddy Linux server will work fine.
Showkase should work fine on a Windows server (I've seen it myself) but there definitely seems to be something amiss with yours and I'm pretty sure that, if you stay with GoDaddy, the way forward would be to migrate (again) to a Linux server.

Please let me know how you get on and if I can be of any further help.
Thank you.

They used that bait and switch routine with me, too.
I used to use them as my domain registrar (I signed up with them for the 'free' email which they asked me to start paying for soon after) but I've since moved on to Namecheap.

Unfortunately, this is pretty much what I expected. If the Server Compatibility Test cannot create a directory, then Showkase simply won't work (and I expect any PHP application which performs any file handling at all will fail, too).
You really need GoDaddy to take a look at their server configuration and allow PHP scripts to handle files and folders (it's probably just a permissions issue hidden somewhere in the server configuration). Without this basic functionality, Showkase is dead in the water.

I still think it might be worth approaching them to ask if they'll switch you over to a Linux server. They don't need to know anything about Showkase or how it works or even anything about what the current problem is to do this. It should be easy for them to do (no knowledge of anything outside of their own services is required) and I'm fairly confident (but can't guarantee) that it would solve your problem. Their Linux servers seem to have better default configuration settings (i.e. more stable with fewer pitfalls) than their Windows servers.

Just for the record, WordPress is free (third-party plugins and themes can be purchased if necessary) and not too difficult to set up. (The most difficult part of a WordPress installation is setting up a database but even this takes only a couple of minutes in the hosting account's Control Panel.).

I wish you well whatever path you go down.
Just let me know if there's anything I can help with.

I just use Namecheap personally as a domain registrar. No problems, though. It was very easy to migrate from GoDaddy (and they were cheaper than GoDaddy's renewal prices, too).
I use the aforementioned free web hosting accounts for personal use (just odds and ends, really, no sites up at present, I only signed up with them because they were free).
I use our own servers (Leaseweb) for testing/business use (probably not ideal for a regular individual user, though).

I wouldn't really recommend a free hosting account (I know you're not suggesting this, by the way) as you may have some or all of the following:
(1) fewer features than a paid account (e.g. the ability to change PHP versions and settings)
(2) limited support
(3) limited web space
(4) more downtime than a paid account
(5) monthly traffic limit

I really just used this to demonstrate that three free web hosting accounts were able to run Showkase without any tweaking at all (so finding a suitable host for a Showkase site really ought to be fairly easy).
The best way to figure out whether or not Showkase will run on a web server is to use the Showkase Server Compatibility Test. It's not foolproof (and you'll need access to the potential web space to run the test) but it might be useful (especially if you use it on a free account before upgrading to a paid account with a new host).

I've really not used any of the web hosts I mentioned extensively (although I've had the accounts for years) so I'd be hesitant to recommend any of them.
AwardSpace is really quick to update PHP (they usually make the latest version available within a day or two of release, even on their free accounts) so they have that in their favor. However, their free accounts have hotlink protection switched on with no ability to switch it off.
x10Hosting has been OK. I had a problem after they migrated my hosting account to a new server (sound familiar?) but they sorted it out fairly swiftly.
ByetHost seems to be the most restrictive of the three web hosts I mentioned, at least with regard to free accounts (e.g. PHP settings locked down, query strings being forced into URLs) but their free accounts still run Showkase (with just one non-critical warning on publishing regarding a PHP time limit which you'd probably never have a problem with unless you had a site with hundreds of galleries).
Having said all that, all these restrictions probably wouldn't come into play with a regular paid-for-account.

Whoever you go with, I'd recommend a Linux server over a Windows server (if you're given the choice). Linux servers seem to be much less problematic.

You're welcome!

Hi.

Unfortunately, I have no experience with IONOS but a (correctly configured) Linux server running PHP 8.1 should be absolutely fine for Showkase (with no need to add backward compatibility for PHP).

However, I cannot guarantee that Showkase will run fine on any particular server (although I see no reason why it should not run perfectly well under IONOS hosting, given the information I have) so, if possible, try running the Showkase Server Compatibility Test on the web space that they provide before committing.

I'm perhaps being a little over-cautious; the IONOS hosting looks fine (there doesn't seem to be anything to look out for). I just can't be 100% certain. Bear in mind that Showkase runs fine on my 3 different free web hosts without any tweaking at all so chances are you'll be fine.

UPDATE:
I have indeed left GoDaddy and transferred the domain registration and hosting to IONOS. Last night I uploaded the SKTest folder and tried to run it and couldn't even see it at the url it should have been at. Everything was blank. I started changing folder and file permissions and still all I could reach was a blank page. I decided to go to sleep and call tech support this morning. Before I did that this morning I downloaded the test one more time and unzipped and uploaded the folder for a fresh try at running. I'm happy to report that the test ran perfect. I'm not sure exactly why it worked this morning and not last night but it's fine. Now I have to go through transferring all the backup folders/files to make the site transfer complete and get it all back up and running again.

So for the record, IONOS hosting on Linux with PHP 8 is compatible with ShowKase.

Now to transfer and update and refresh my site.