Sounds like an issue ive had, Did you try to take out a Ram card and or Replacing the ram card?
Heat, dust, corrosion eventually makes ram fail which leads to the system failing to boot.
As you said "nothing on screen" id give that a shot. if there is only a single ram, take it out and boot it should make the system make a *change* then re insert the ram and attempt to boot. If that doesn't work try taking out the Bios Battery + Ram and hold the power button for 20 seconds, It will reset the CMOS. Install the ram again and re insert the Bios battery and attempt to boot.
The Bios Battery is a Small but Large "button Cell" style battery located on the motherboard and is usually found near the Hard Disk Drive.
Let me know if this helps.