Re: Hosting change: impossible to login or register.
Cookie issues? Have you tried clearing all the cookies?
Also, there are probably places in the database that have references to file system paths and things like that (I know WordPress does this, for uploads for example.) Maybe there is something in the bbPress tables like that that is preventing it from working correctly?
What I usually do is search the tables for a string that was unique to my old host (a customer number or something else in the path that is unique) then once I find those records, I do a global search and replace on the whole string.
Maybe it’s something like that. I don’t think the database dump will just work straight-away on a new host without modification.