External hardware can be an issue,if you have any external hardware such as a printer,external hard drive,web cam ect,unplug them all...Only have your keyboard n mouse connected,now reboot the computer......I asume you have tried this already.....
You dont need the rubber gloves.....Nore the wellies....
Power off the computer,remove from power outlet on the wall.....Open her up and touch the power supply for a few seconds.....This should eliminate static......Locate the reset jumper on the mainboard usaly by the BIOS battery and remove and place on the two empty pins,count 10 and replace onto the two origonal pins,reboot....
If your using a wireless keyboard and mouse I sugest until we can resolve your issues switch to a PS/2 keyboard and mouse,....
Then are you able to enter BIOS and check the time and date is correct?
Wrong time and date can stop a computer from booting....
Have you tried the one stick of RAM in at a time?
This may not be hardware but as Nev said it just is not starting up,have you ever updated the BIOS?