Or you could have all the voltages, but there's something wrong with the "Power Good" signal from the PSU to the motherboard. If that's not right, even with all the power voltages present, your PC will not boot.
Work the checklist. Then, if the PC still not working, the best way to test the PSU is by substituting a known good one of similar capacity. Brand new, out of the box, untested is not a known good one.
Breadboard - that will isolate any kind of case problem.
http://www.tomshardware.com/forum/262730-31-breadboarding
Breadboard with just motherboard, CPU & HSF, case speaker, and PSU.
You can turn on the PC by momentarily shorting the two pins that the case power switch goes to.
You should hear a series of long, single beeps indicating memory problems.
Silence indicates a problem with (in most likely order) the PSU, motherboard, or CPU.
Next best thing is to get (or borrow) a digital multimeter and check the PSU.
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. 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
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. You can carefully probe the pins from the back of the main power connector.