You can use a paper clip to ground the power switch wire (green) to one of the 'ground' wires (black) momentarily. This will cause it to turn on (or off, if it's already on.) Don't leave the paper clip in there, since this may cause some PSUs to switch on and off repeatedly, potentially damaging something.
Note that some PSUs do not like starting up with no load attached. Also, this won't tell you if the PSU is actually outputting 'good' power, or can take its rated load. In theory you could check this with a voltmeter, but you may not get accurate results with nothing hooked up.
The last time I was at CompUSA I saw a PSU tester that at least claimed to check the voltages (it had little red/green lights for +3.3V, +5V, +12V). No clue how well it works.