Now if you do NOT get any of the above, as another reply indicates,
you will get this symptom if your motherboard is blown.
As to your PSU, which COULD be the problem:
Open your system (with power off of course) so you can see the
motherboard. Turn ON. Some motherboards have LEDs that light for
each DC voltage (+5, -5, +12, -12, and some have a +5 Standby), see if
yours does. By the way, the +5 Standby is the LED that stays on even
when your system is shutdown (as long as AC is on to your PSU), it's
like the standby on your remote TV or Surround Sound System.
As other replys say, you can use a multimeter to check your PSU
voltages, very carefully, at the Main Power Plug and the separate CPU
Power Plug (4-pin, brown/yellow wires). Below page has a very good
pin-out diagrams: http://en.wikipedia.org/wiki/Computer_power_supply
======== Tecknomage ========
Computer Systems Specialist
San Diego, CA