I am not an experienced tech person, so please be gentle.
I am the nominal webmaster of a group blog. We had been running on an older version of WordPress (pre 3.5). We could not upgrade because we were on MySQL 4. Last time I was in our host's control panel, a pop up appeared allowing me to upgrade to version 5. I did and the blog immediately collapsed (Error 500). I tried a fresh auto-install of WordPress but no luck. Obviously I don't have access now to the wp-admin dashboard to do a normal export.
Our (cheap) hosts say there is nothing they can do to restore it.
Have I lost 3 years' of colleagues' work, or can we reinstall from the database we have? Is this database compatible with the latest version of WordPress.