It looks like the host for this site has changed owners, and the new owners have been changing some things around.
 
One of those things is the licensing for plugins we were using for:

• Uploading files,
  
• Resizing images, and
  
• Sending emails
  

I'm looking into a workaround now...

UPDATE: Gallery images can be viewed, but not uploaded yet

So the host got back to me.
 
They're not going to renew the licenses for the third party software that used to exist on the old host.
 
Currently, the following doesn't work:

• file uploads,
  
• image resizing or image captions,
  
• sending emails (including the contact page, signups, and message notifications)
  

 
I'll make an effort to get the emails working using a different method, cos that's pretty important!
 
As for the rest, f**k 'em. I've been (very) slowely rebuilding the site in a more modern responsive design as a kind of learning experience. I'll just have to accelerate that project.