OS X Technologies :: Time Machine Just 'stops' Copying Data

I have Time Machine set up to backup my laptop, and it works just fine. I then decided, having enough space to spare, to point Time Machine of my girlfriend's laptop to the same backup location (she had been backing up to an external drive).

After setting everything up (network location, password, and everything), Time Machine happily starts backing up: Until it just stops copying/transferring data. 

I start with a fresh, new, clean backup and I get no error message of any kind; after Time Machine selected the files to back up (= first run, so everything gets selected; that's about 40gb) it starts copying everything. But then it just stops. No errors, no progress, no anything.

This usually happens after having copied between 1 and 3 gb (I tried multiple times). Being on a gigabit ethernet, the copying is pretty fast; the first gb takes minutes. I even proceeded to letting the laptop run its backup through the night; even after a dozen hours, the indicator still is stuck at "1.27 gb of 40.24 gb" (or whatever). 

I went so far as to check the laptop's hard drive (no errors). The backup system appears to work just fine; after all, Time Machine starts the backup just fine and doesn't report any errors or issues. (Also, if there was something wrong with it, it shouldn't work with my own laptop, either.) The only difference I could think of is that my laptop runs Lion, while my girlfriend's still runs Snow Leopard (both to their respective newest versions; could this discrepancy be the cause of any incompatibilities?).