I had a similar issue before, here is what I found.
The lights you get typically indicate +5 volt standby power is active (typically a purple wire) but this circuit is on a different section of the power supply than the big guns so to speak with your 5 (red) and 12 (yellow) volt rails. If any of those fail then the computer will not start due to lack of power. To my knowledge there are no error codes for this since the computer doesnt even begin any self checking since it cannot even start initial power on.
For my case I found that bad capacitors in the CPU power supply led to the destruction of one these rails due to overloading, overheating, and then arching on both the motherboard and inside the PSU. I have to admit it was a rather spectacular failure.
Now if you are lucky then only one component is to blame.
As for testing the motherboard, see if you can borrow a powersupply for a buddy or use a known working spare and see if the system starts up, if not then you need to look at a replacement motherboard and possibly memory and/or CPU. Power issues can be really mean when they occur, case in point a brand new gaming rig with an FX series CPU and SLI had an issue on initial boot, and every component got wasted.
A trick that I have seen work in rare occasions was pulling the battery and resetting the cmos for an extended period of time (15 minutes or so). This should not change anything but I have seen them mysteriously come back to life and continue working without a single glitch.
To see if all is not lost here's a quick and dirty way of testing a PSU.
To test your PSU, take it out of the case and see if it passes the sniff test, if it smells like "unholy electrical death" (yes that is a technical term) then you know that it's bitten the dust. If you have never had the joys of first hand experience in releasing the magical blue smoke that makes transistors and other components work, compare the smell to that of a known working rig, if the PSU smells worse then its gone.
Providing the blue smoke hasn't been let loose, you can turn on the PSU by shorting what is typically the green wire to ground, consult your documentation for what is the PSU On wire, not the pwr good wire.
If all your voltages are within spec and you happen to have a few car tail lamp bulbs (the 12 volt non LED variety) around, see if the 5v and the 12v rails can keep the bulb lit for more then 5 seconds, if yes then the power supply should be good to go.
Note, the 12v test will make the bulb MUCH brighter then the 5v test
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