Yep, I've got 3 of those (left). One has its insides caked in dust, but still works just fine. Unfortunately they do have rather weak rails, so if you do come close to overdrawing on that 250W limit, they will blow up (evidence being a pop and black smoke, not always in that order). That's happened 3 times to me, although once was my fault for plugging it in at a wall with an incompatible voltage (the difference between 120-something volts and the 260-something volts the UK has - I've long forgotten the specifics). EDIT: To make it clear, that PSU does not need any airflow since it's not supposed to create enough heat to need it (a bit like old CPUs) - plus it's also such a low power rating.
For your old computer, it's probably all the computer needs, and the chances of it causing your problems is around 23% (educated guess). If you upgrade to anything modern, it's only a bit over half of what you need (450W is the minimum recommended for the average budget system these days).
