Cheex:
any component can fail at any time, even new power supplies. If you check Newegg user comments on different power supplies some people have complained that their power supplies literally smoked shortly after turning them on. (Cheap brands)
The power supply for your Socket A system should work with the 775Dual-Vsta, as long as it has the 4-pin power connector (2 yellow, two black leads). The power supply I'm using on my ASRock is the same I used on my old Socket A motherboard (Asus A7V).
You can also try putting your new power supply in your old system. (There an extremely small risk that a bad power supply can damage the motherboard but that would be extremely unlikely if you bought a good brand power supply).
What I would try next, before even switching power supplies, is to remove every single card from your motherboard, including the video card and ram, and unplug all the drives. (Make sure power cord is unplugged whenever you remove or install components).
Then try to turn the computer on to see if the fans turn with everything unplugged. If the motherboard is still dead plug in the ram and try again.
If still dead I think I would try swapping power supplies next.