I would have to say that a five year old Vaio (with a five year old HDD in it) is only marginally better than no backup at all, given the age, likelihood of failure, and the very un-straightforward way of connecting to a share--of limited size--to save some files. While not particularly difficult, it still requires having a separate machine & OS booted, connected to the network, attaching to the share on the Mac, and then finally moving the files. Definitely not a good everyday solution for backups.
If there is ANY way you can scrape up the $$ to get an inexpensive external (the WD's are stupid cheap--as little as $139 for a 320GB drive) that will be dedicated and "just plug it in and use it" simple is by far your best bet.
While the Vaio may work for a short time, I'd suggest start saving up for a dedicated drive soonest.