The gray wire is not a power output. So the +/- 5% tolerance does not apply to it. It is a control signal that goes to a Logic HIGH (greater than 2.8 volts, but typically 3.5 - 4.5 volts) when the 3.3, 5, and 12 volt outputs have stabilized. The computer needs this signal to boot.
If the PSU is working properly and the gray wire is sitting at a Logic HIGH, you have the 3 main outputs present.
If you have only the CPU & HSF and the motherboard connected to the PSU and you try to boot, you should hear a series of long beeps indicating missing RAM. Silence indicates, in probable order, a bad PSU, motherboard, or CPU.
At this point, you can sort of check the PSU. Try to borrow a known good PSU of around 550 - 600 watts. That will power just about any system with a single GPU. If you cannot do that, use a DMM to measure the voltages. Measure between the colored wires and either chassis ground or the black wires. Yellow wires should be 12 volts. Red wires: +5 volts, orange wires: +3.3 volts, blue wire : -12 volts, violet wire: 5 volts always on. Tolerances are +/- 5% except for the -12 volts which is +/- 10%.
The gray wire is really important. It should go from 0 to +5 volts when you turn the PSU on with the case switch. CPU needs this signal to boot.
You can turn on the PSU by completely disconnecting the PSU and using a paperclip or jumper wire to short the green wire to one of the neighboring black wires.
http://www.youtube.com/watch?v=5FWXgQSokF4&feature=youtube_gdata
A way that might be easier is to use the main power plug. Working from the back of the plug where the wires come out, use a bare paperclip to short between the green wire and one of the neighboring black wires. That will do the same thing with an installed PSU. It is also an easy way to bypass a questionable case power switch.
This checks the PSU under no load conditions, so it is not completely reliable. But if it can not pass this, it is dead. Then repeat the checks with the PSU plugged into the computer to put a load on the PSU.