Here is a series of troubleshooting steps from member TVeblen.
You should be able to adapt them to your situation.
Strip it down and then add components back, one at a time, to try and isolate the offending component.
The test (power off, power cord unplugged):
• Disconnect everything externally connected except the mouse and keyboard (printers, USB devices). If you are not using a wired mouse and keyboard see if you can borrow one.
• Disconnect the power and data cables from all the drives inside the computer (Hard drives, DVD/CD drives).
• Remove all the cards installed in the PCI slots including the video card. (be careful handling them and place them on a non conductive surface while testing).
• Remove all the RAM sticks (same rules as above).
Now connect the power cord and turn the PC on.
• The motherboard should start beeping. You should get a beep code that tells you there is no memory. This is good, it means the processor is functioning and the motherboard is good so far.
• Now add one stick of memory in Slot A1 and power on. More beeping: "no video card" beep code. This is good.
• Then add the video card and connect it to the monitor. You should get no beeping and you should see the BIOS screens, ending with the message that there is no boot device.
If you get no video then switch the one memory stick installed for another one and test.
Continue adding components one at a time.
If at any point the PC fails the the last component added was the problem one.
If you removed everything and there is only the Motherboard (with integrated video), processor, and power supply to contend with and it does not POST or show anything on the screen, then the problem is one of those three.
If you have tested by using another power supply then you are down to two. CPUs rarely fail, so motherboard is the most likely guess.
Try performing a CLRTC or Clear CMOS as a last ditch effort, and check the 3v battery. Both long shots, but what do you have to lose at this point.