Martin,
sounds like a bit of a mess in there. Firstly, how did you upload the website to the new host? It sounds like you have a pretty good idea of what's what but you might want to check if the images went up in binary, and the html, and exe files went up in ASCII.
If that works, you might want to grab one of those .jpgs, and load it onto another server (like a free account at Xoom or something) to make sure. If all is still well, it sounds like a problem on the server. Have them check the configuration to make sure the file types are doing what they should be doing. That's a long shot, but I'm just brainstorming.
Failing all of that, a webhost should offer some solutions before blaming the client

If you can, pack your bags and move somewhere else. Moving is never a pleasure, but a poor host is worse. There's plenty of us out there who'll try to look after you a little better.
Greg Moore