Sounds like a rock and a hard place. System is certainly out of warranty, and as it was on the super low end 6 years ago it is probably not worth throwing any money at it.
You could buy a new 150W PSU to try and get it up and running again, but in all likelihood the PSU probably took out other parts with it, so then you are probably looking at a new motherboard... maybe ram and HDD... possibly a CPU. And if this is something like a Dell or HP then you probably can't go out and buy standard ATX consumer parts, you will have to look for parts that are specific to your machine.
If I was in your shoes here is what I would do:
Find a nerdy friend who has a PSU you could borrow rather than buying a new one (or 'borrow' a PSU form another...