Hey MrWiggles,
Do you get a POST signal? If not, try checking these before calling the PC dead.
Check CPU Fan and that is attached to the power outlet for CPU fan and that it spins when power is turned on (Some motherboards cannot POST if CPU fan fails to report active).
Clear the motherboard CMOS, by looking in the motherboard manual for how to do (Usually removing the battery for 15 minutes will solve the issue)
If using jumpers to overclock your machine (Voltage and Multipliers) then put the machine back to default setting or jumperless
If nothing fixed, then make sure the PC Speaker is attached properly and listen if any beep-codes and if so consult your motherboard manual for the meaning
Clear the cabinet from dust, as it might cause short circuit.
Take out and reinsert all devices like PCI, AGP and memory modules in case of a bad connection.
If still no beep codes, then one have cut down the problem area
Pull out all unnecessary PCI cards, leaving only the Display Adapter
Pull out all but one memory module (Make sure that the one is working)
Pull the power from all HDD, CD-ROMs, DVDs.
Reboot and see if problem is fixed, and if so plug each pulled out device back in one by one.
If nothing fixed, pull out the Display Adapter and the memory module.
Reboot and see if it gives beep codes, if so consult your manual for their meaning (It might be caused by faulty memory slot or incompatible memory module)
If no beep codes when only having the CPU attached, then pull out the CPU.
Reboot and see if it gives beep codes, if so then something might be wrong with the CPU or the CPU temperature
If no beep codes with a clean motherboard, then try another power supply (Which is known to work)
If no beep codes then try to remove the motherboard from the case and check that no metal objects like a screw or bare wire is short circuiting.
If still no beep codes then there is the following possibilities
Ram
Video card
PC Speaker
Power Supply
A bad or corrupt BIOS flash
Motherboard is dead
After that, I do not know what could be causing the issue with your PC.
Good luck.