Possible trouble with Processor

If the CPU was dead you would have had definate indications. Memory checks would not perform, hard drive would not "power up", it probably boots you just can't tell, maybe. However an overheated processor can cause system problems. (1)After the PC has been running for a while, open it up, and turn it off. Then ground yourself and touch the processor carefully, or part of the heat sink near the processor.If you cannot leave your finger on the processor for more than a few seconds due to the heat, the chances are that the CPU is overheating. Was this pc working before and suddenly this? What preceded this event if it was working before? Are you using integrated sound or is an adapter board installed.
(2)See if you can bring up the bios setup screen. That will answer a few questions such as video and CPU problems.
(3)Use the integrated video output. You will need to turn it on in bios setup.
(4)Remove all optional devices from the motherboard, including expansion cards, external peripherals, etc. and see if the problem can be resolved.
(5)Reset all BIOS settings to default, conservative values to make sure a BIOS setting isn't causing the problem. Set all cache, memory and hard disk timing as slow as possible.
(6)Turn off BIOS shadowing and see if the problem goes away..
Double-check all connections to the motherboard.
(7)Check inside the case to see if any components seem to be overheating.
(8)Inspect the motherboard. Make sure the board itself isn't cracked;
(9)Make sure no broken pins or components are on the board; if there are, you will have problems with whatever component of the PC uses that connection. Check socketed components that may be loose in their sockets. (10)Did you try another monitor? Does the light on the monitor change color, probably green, as pc tries to boot?
You have a vague and wide spectrum problem, it could be anything so you need to eliminate many things. Keep a log of each step. I do not suspect a CPU failure.

Try removing and re-seating the RAM modules.

Since you have no video, I assume that you also are not getting into the POST, so you do not know if ANY component is good.

After re-seating the RAM modules, remove any modem or network cards and see if the PC now POSTS.

If it now POSTS, replace the modem or network card.

Next, try resetting the CMOS memory.

If you still have no POST, then it is likely either the motherboard or CPU is bad.

The CPU is the easier part to swap.

Chas

I've found CPU's to really last. When their introuble you often will boot up and later you get weird random errors.
The machine is clearly not Posting properly. I would first Check the Power supply. I.E. Substitue it and see. Also Check the memory sticks, if your using Rambus or some of the other high speed sticks especially.

Check the Mboard if needed by pulling it out strip down to Video only and a speaker and see if it starts.
Just had one where the second Hard Drive would kill the Mboard in this fashion and it would not reset until the jumper was used to reset it.