This sounds like similiar problems that I had just a few weeks ago.
The computer patient was a HP 3.0 Pentium 4 with a gig of DDR Ram with windows xp Media center edition.
Before you sink money into fixing a computer, ask yourself "Is it worth it or time for an upgrade to a better machine?".
This computer stopped working during a Thunderstorm!

The Battery Backup that it was connected to sounded an internal alarm just as the power went out and the thunder sounded. It passed a surge and the computer froze. It would not boot back up once it was powered down.
I figured it was toast, so it was time to buy a new one. It was replaced with a quad core pentium 6066, 4 gigs of DDR ram, 750 gig hard drive, and alot of other goodies in the form of a New HP Tower.
Recently, I got to thinking about the old one and decided to see if there was a chance of bringing it back.
First thing to check, Is the machine following the boot sequence of the BIOS?
Determining this can and often times will lead you in the general direction of the problem.
If the BIOS on the motherboard is active and working, it will first light up the cd/dvd drive to see if there is a disc it should be booting up from. Then it will start the hard drive and boot up from there.
Is the hard drive spinning? You should be able to hear or feel a humm coming from it if it is.
In my case, it passed all of the above. The hard drive was running but nothing on screen.
After disconnecting and testing the power supply, it passed also.
In almost every computer brand, you should get 3 different voltage levels from the power supply. 3 volts, 5 volts and 12 volts.
Don't worry about checking every wire for voltage. Each voltage level picks up power from the same spot inside the power supply.
I then began to check cards, thinking it was the video card.
Video card looked fine, but the modem didn't. There were several chips on it's board that had the center exploded out of them.
AAAAHHH, point of entry for the power surge. I'm hearing this is typical.
I removed the modem, and it booted up!
BUT..............there's always a but.
It wouldn't get on the net because the onboard ethernet adapter was dead. So I intalled another ethernet adapter into a pci slot. No Dice.
After some testing, I realized it could not communicate with any of the PCI slots. The PCI Bus on the mother board was dead/damaged.
I purchased a new motherboard for $65 and installed it along with another gig of RAM.
Now it works like the day I bought it. I believe I got lucky, but I'm also very happy to see it back again.