Question : Problem: Computer not starting; no BIOS, no beeps, but fan works.

Problem:
     I have an Alienware desktop (1 yr. old) that recently crashed while playing a game (Half-life), I heard a loud, continuous beep through my headphones when it froze & I hit the power switch on the front of my comp.  
     When I tried turning it back on, I got nothing; the display showed a blank screen (but not the "No Signal", just blank), the yellow LED light on the front lights up & flickers, I see my DVD light flicker (it also opens when I push the button), and my fans all work (2 rear, 1 side), but the green LED light on the front of the case stays dead.

Troubleshooting:
     I have an identical setup so I was able to swap & test.  I frist tried swapping the RAM w/ no effect, then I tried the video cards, then CPU.  I couldn't get the HD off of the working comp, so I just tried unhooking both HD's and the working comp went to BIOS while the broken one just did what it had been doing (nothing).  I've also tried switching the thick black power cord.      
     I could see no visible burns anywhere on the motherboard, however I noticed some amount of static electricity on the chassis; enough where I brushed the inside of the case with my forearm and thought I cut myself slightly.  The case was not opened while it was running & subsequently crashed.  My computer is sitting on a rug ontop of a tiled stone floor (which my house's entire flooring is covered with).

Specs:
     CPU..............dual Intel Pentium 4 3.06GHz
     Memory........1024MB
     HardDrive......80.1, WDC WD800JB-00CRA1
     DVD-Rom......Samsung DVD-Rom SD-616T
     OS................MS Windows XP Home Edition
     BIOS.............Award Software, Inc.
                         ASUS P4T533-C ACPI BIOS Rev. 1
                         ASUS   -42302e31
     Video............ATI Radeon 9700 Pro (128MB)
     Sound...........Creative Labs Sound Blaster Audigy 2 Platinum
     
Conclusion:
     From what I've read online so far (not much), it seems maybe my motherboard or powersupply is shot.  I haven't tried taking out my CMOS battery or changing powersupply or motherboard yet.  Your help is appreciated (but the max point value I can give is 500), thanks in advanced.

Answer : Problem: Computer not starting; no BIOS, no beeps, but fan works.

>>>"Based on your indications the power supply sound okay." Not sure where rcmb got this idea. I have to strongly disagree.

The fans run on 12v the power supply has 3 voltages 12v 5v and 3.3v. If you loose the 5v or 3.3v it can still act as if it is powering up.  What happens is you don't get power to ram vga or cpu. this is why when the PSU dies or is weak you usually don't get any post warning beeps or video.

Change the PSU with the known to be good unit to be sure. The other testing is good but you should start with a known to work PSU.

This is how I check a PC that will not post. Remove All unnecessary hardware. But Cpu RAM and video card.  Verify power supply is working (very important step).  Verify System speaker is properly attached.
If no go and no beeps replace cpu with a known to work cpu or test on known working system
If no go and no beeps replace motherboard.
By now you should  get POST or a warning beep of some type.
Be it ram or video.