What is wrong with power supply installation?

Recently, my computer has not been able to turn on. When I turn it on the power supply starts going for about 2 seconds (fans turn on) and then stops. I brought it to a computer repair store and they looked at it and said my power supply is basically too weak right now to power up my hard drive (500GB). So, I bought a new one and installed it and now it won't power up at all. I tested it on a power supply tester and it is still good, and tried another power supply as well. Furthermore, when I plug in my old one, its still tries to power up as normal for a few seconds. Therefore, I know my connections are all good. Oh yeah, my voltage is set at 115, so its not that either. Any ideas why my old PSU still revs up, but the replacements won't.