backing up master db won't affect no of locks held, though it is something you should be doing on a regular basis!

use sp_lock to see how many locks are taken out.

sounds like you have /3gb switch enabled or this is 64 bit? I would look to up the amount of physical RAM you have if possible.

Are these processes hung or just long running? Whilst they remain active they will hold onto their locks (possibly causing blocking) so investigations into what is happening to these connections will be worthwhile.