PC won't boot cold, requires power on and THEN a hard reset??

[pocketExistentialist]

Hello, I've had a problem with my PC for awhile. About 20 months ago, I did a complete overhaul of my PC and upgraded the mobo, CPU, video card, RAM, and HDD. It worked for awhile, but then about 3-6 months after (not sure exactly when), I started having a funny problem... When I start the computer from a completely powered off state, the fans start up and everything, but the display stays blank and the computer doesn't actually start booting. It usually requires me to hit the reset button (which is annoyingly small!) Even worse, when I take it to a LAN, or bring it back from a LAN, it usually takes 10 or more reboots and me unplugging the power cable in the back several times! I figure it's a problem with the motherboard or the power supply, but I'm not sure and I don't want to just go out and buy one unless I am fairly sure about it. This issue has been getting to me more and more lately, and any help would be appreciated. Here's the low-down on my PC specs, and keep in mind that I actually bought Alienware about 3 1/2 years ago (back when I was a spoiled rich kid who was hardware-phobic), so the PS has been in use for awhile.

Athlon T-Bird 1200 Mhz w/ 133mhz double pumped FSB (9.0x133)
ASUS A7M266 (AMD761 chipset)
256 MB PC2100 DDR RAM (don't remember which brand)
Leadtek GeForce2 Ultra
SoundBlaster Live! Value (not 5.1)
IBM DeathStar 75GXP 75.0 GB (running 20 months 24/7!!)
Pioneer DVR-104
AOpen 16x DVD-ROM
Netgear FA312, Linksys NC100 Ethernet cards
300-Watt Power Supply from an Alienware computer (don't know what brand, I never checked)

Thanks in advance for the input.