WARNING: LONG STORY AHEAD
If you want to skip to the point, here it is: I think it might be the video card. Read below to see why.
Let me preface this by saying that I'm not a hardware expert by any means. If anyone out there can contradict my logic and prove me wrong, PLEASE do so (I just want the damned problem fixed). That having been said, I'm having the exact same issue. Here's what I've been able to figure out:
I started with an AMD 1.33Ghz T-bird in an old Gigabyte mobo. Had a weird problem where the machine didn't like to POST after a soft-reboot. I'd get exactly the same symptoms... power comes on, fan and drives spin but no video POST and the monitor just never received a signal. Finally I broke down and bought a new Mobo, figuring that my old one's BIOS was shot.
A friend and I (who knows a lot more about hardware than I do) started from the ground up... new case, new PSU (350W EnerMax), new 258MB DDR-RAM, new Mobo (Asus A7N8X). The only three components we kept from the old machine were:
THE SUSPECTS
A) The video card (GeForce 2Ti that the fan had siezed on)
B) The CPU (AMD 1.33Ghz T-bird purchased second hand)
C) The hard drive (freshly re-partitioned and formatted)
So we slapped everything together and powered it on and what do you know, but it starts doing the same thing as the old one after just a couple of boots (it locked up in Windows). I could get it to POST usually if I unplugged the power and let it discharge for about 30-40 sec, but when it did it would try to run the CPU at 1000Mhz and the self-check would display a message like "Due to improper shut-down, the system is running in Safe Speed. Enter the BIOS menu to change speed settings."
Well, when you save and exit BIOS it does a soft-reboot which produces the same symptoms you're describing. Anyway, long story short, since the problem occurred on both Mobo's I'm inclined to say that's not the problem and I can further infer that it is one of the three aforementioned Suspects.
I highly doubt it is the hard drive, since the HD has nothing to do with system POST. That leaves the CPU and the video card... the CPU had run smoothly for a good while before problems started, and POST'ed ok on a machine at the local PC doctor. The video card is very questionable, since I have no idea how long it ran without a fan. I also noticed that the vid card's BIOS chip sits right next to the heat sink. Its not beyond the shadow of a doubt, but my money is literally on the video card. I've ordered a new GeForce 4200 which should be in tomorrow, so we'll see... I'll post when I know something.
There... glad you read the long version? LOL.