I don't know if this helps you troubleshoot or not, but I have another album on this same site and I just tested it and it works just fine. I run the site for an organization I belong to. There is some public web pages, then a section that is for members only. This area is basically punbb and a coppermine gallery. They are bridged and in a subdirectories.
Then I have another gallery that is just for me where I put family photos to share with family. I am the only user of this gallery. It has its own database and is in its own subfolder.
All worked fine though I haven't used it for a while. I tried to upload a file yesterday and it didn't work, I got the same behavior I am getting now. The gallery was 1.3.x and I figured I wouldn't get any support for that here so I upgraded it to 1.4.x. That doesn't work at all now and I have a thread going in the upgrade area to try to fix that. In the mean time I decided to do a fresh install in yet another database and another directory. That is this one that works a bit, you just can't upload files.
So to recap:
Coppermine Gallery for my organization, 1.3.x -- working fine
Coppermine Gallery for me, was 1.3.x, but wouln't allow uploads so I upgraded to 1.4.x -- doesn't work at all, displays fatal error
New install of Coppermine Gallery for me 1.4.x -- can't upload files, this is the one we are discussing here and that you looked at here.
Again I don't know if that helps in any way, but to my uneducated mind it says that it isn't something my web host did or it would have broken the other gallery too. But, I fully admit to being less than a novice so that might not be right.