Whenever I try to backup a database it goes until 90% and gets stuck there until I manually kill (because it doesn't stop if I try to stop it) the msftesql process.
That clearly means that something makes a conflict between the fulltext indexing and the backup process.
So, have you seen anything like this? If not, how would you go about debugging this problem?
The first and obvious debug point is to disable full text indexing and try backing up the database again. If it does backup, then you know that FTS is the problem. If it doesn't, then you have another issue to find.
I would also check both the SQL Logs and the Event Viewer to see if any useful information is there.
Finally, if you have actual, physical access to the server during the backup, listen and see if the disk is making any funny noises during the backup process to indicate a disk failure of some sort.
I can say that I've never had FTS stop a backup from happening, but that doesn't mean it couldn't happen.
What time do you happen to have the job that refreshes the Full text indexes running? Perhaps it is trying to repopulate those indesxes at the same time the backup is running.