Firstly, if you're computer beeps or gives any other error code, look it up and fix it accordingly, the guide below is for the FF error code or if the computer won't POST at all.
The dreaded "FF" POST code, or no POST at all (this fix is best done outside a case to ensure the case isn't shorting the motherboard):
1) If you know what burnt electronics smell like, then smell your motherboard. I'm not joking. Specifically around the VREG (left/above the socket), Southbridge (below the socket) and Chipset (right of the PCI slots) areas. If you smell burnt electronics, keep that in mind if you hit step (7b) below as that'll means its the motherboard 99.9% of the time.
2) Test the PSU with the tester, if it's not beeping/blinking at you then it's ok (if you're using the one I linked). Unplug and re-plug the 24-pin connection several times. Keep an eye on the "PG" and see if it ever reports 0ms or 999ms as this means it's a bad PSU (since this is unloaded it won't fail the PSU tester every time even though it will fail the motherboard every time). If you don't have the PSU tester, swap in your known-good PSU.
3) With the PSU verified to be good, plug in ONLY the power to the motherboard (20+4-pin and 4/8-pin CPU power, but NOT the 4-pin molex connection if it has one). Disconnect EVERYTHING else from power (hard drives, DVD drives, etc).
4) Remove all RAM. Remove all GPUs. Remove all other PCI/PCI-e cards. Unplug all the cables (including SATA, IDE, FDD, SAS, USB, Firewire, HD Audio, and all the switches but the power switch) from the motherboard. You should have just your MoBo, CPU, HSF, PSU and a power switch connected right now. Disconnect EVERYTHING from the front and back panels of the computer, including your mouse and keyboard.
4a) if your computer does NOTHING when you hit the power button, plug the reset switch into the power switch pins on the motherboard and use the reset button in case the power button has gone bad - yes, it happens, no it won't damage anything.
5) Remove the BIOS battery and leave it out until you're told to put it back in.
6) Power on the computer. If it beeps or gives a POST code other than FF then go to (7a) below, if not check out (7b)
7a) If it beeps at you, or gives any POST code other than FF then turn it back off. Leave the BIOS battery out. You will now add in 1 piece of hardware, power it on, check if it POSTs (and gives any error other than FF), if it does, turn it back off and add the next component. Start with RAM, one stick at a time, then GPUs, one at a time, then other expansion cards, finally HDDs/DVD drives - rebooting between each and every part.
8a) If it starts giving an FF code or stops POSTing all together then the last component you added is bad.
9a) If it doesn't give a FF error code and is still POSTing with all your hardware back in, shut it down again, put the BIOS battery back in and power back on one more time. If it gives an FF code now, replace your BIOS battery.
10a) If it works with everything back in, then your motherboard lives to fight another day.
7b) If it still POSTs as FF or not at all in this condition remove the CPU, make sure the pins are intact, reseat the CPU and HSF and try it again. If it still posts FF you either have a bad motherboard (about 95% of the time or about 100% if you smelled burnt electronics in step 1) or a bad CPU (about a 5% chance).
8b) Swap in a known working motherboard if you have one to test the CPU is good, or bring in a spare CPU to test the motherboard with. Whichever part fails is the culprit, replace it and go again.