You can almost rest assured that Compaq isn't like Dell, who rewires their PS's because it's "better" than the ATX standard. And if they did, your PC would be dead because of incorrect voltages going to the wrong places in your computer.
A couple things that could be preventing your PC from working are the P4 connector, a short, a dead power supply (try plugging in your old one; if it works... guess what!) Since you didn't take the mobo out I'm assuming, it's probably not anything to do with that.
Experiment, because it's only 200+ volts and however many amps, right?