Testing a power supply without hooking up its intended load
I'm not too familiar with computer PSUs, but I can offer a few things that I think might help.

1) Look at the specifications for your intended load. In a datasheet or specsheet there should be a power draw spec or at least an operating voltage and a range of possible current draws. This allows you to look at the worst case(most power absorbed by load) and best case(minimum power absorbed by load). After doing so, you could create a resistor network on the output terminals you're interested in that draw the same power. It's important that you choose resistors suited for that power draw, otherwise they're going to overheat. 

2) If you want to do it empirically, you could connect a network of potentiometers (each with large values) in series, and you can connect them so that they are all at the highest impedance at first. This would essentially simulate an open circuit, so you would have close to zero power draw. After doing so, you can very gradually, one by one, lower the resistance of each pot (from highest impedance to a short) until you can see that the power supply is switching on. It's important that you never try to draw more power than allowable by the PSU though, as this will damage it, so make sure to check the spec on max power for your PSU.

I'm making these assumptions based on my usage with general power supplies on lab benches. I'm not sure about the specifics of computer PSUs, but it's strange to me that the power supply refuses to turn on without a load, seeing as an open circuit shouldn't damage the supply in any way I believe. This is a reach, but it sounds like your power supply is somehow shorting without a load (maybe internally) that's causing it to not turn on, maybe as a short circuit protection mechanism. This probably isn't the case seeing as it works with certain loads. Hope this helps.