I would agree with the above, in terms of a password change on the BE account being a distinct possibility.
One other recommendation I would make, is to try and sell the client something like an Iomega stor center NAS box ( < £200), and configure the built in Window SBS backup utility to do a scheduled backup to the NAS box ( say at weekends). That way even if they forget to do the tapes down the line you will hopefully have some kind of backup. We do this for most of our customers now - I always like to have more than one type of backup if possible, and ideally with different software.
The other thing worth checking is, if the backup hasn't been working, then the exchange logs will be eating into disk space. If you haven't sorted the BE account problem yet, just make sure you're not about to run out of disk space on the C: drive ( which is the default for the exchange, but it could have been moved).
kevin