Agreed.
If you open the case and there are NO lights at all it's likely a dead PSU.
As for buying a PSU, you need to see what's compatible with your case. Probably a normal ATX would work.
As for power, look at your current PSU and buy one with more power. For example, if it's a 260W get a 450W such as a Corsair or Antec.
Basic troubleshooting involves swapping parts. Considering how much it costs to repair a system, spending $60 on a PSU first is the best step.