Could clarify that the blog does work properly with the default Twenty Ten or Twenty Eleven theme? Also if you are using plugins you should probably say which one(s) are active.
The theme should be ok unless it is really out-of-date which it looks as if it is (last updated in March 2010). They really only style and layout the content for the most part but if the core code has changed and the theme isn't updated you'll have a problem. If the default theme works then I would say you need to choose a new theme, something that is recent and well supported.
I would start by looking here. Smashing mag has been around for a while and they aren't quick to put their name to shoddy content. These themes should be a good place to start, you could look in the comments below the post also. You really want to know that whatever theme you use is going to be around in another year or two.
If this approach still generates problems then I'd go back to the host and try to get some more help. Hosting is cheap you could always find one that might help you a little more if your blog means that much to you.