Failure to POST

I just built a PC for my kids for Christmas. Though generally happy with the entry-level system, I'm having intermittent problems with the machine failing to POST - the power LED lights up, the HDD led blinks once, then nothing... The PC stops doing anything with no beeps or other light flashes (the monitor never even turns on). As of right now, one push of the reset button has always cured the ailment. Though the problem seems to come and go, I'd speculate the average is about 1 in 10 starts that experiences this hang-up. I've built other PC's, but never experienced any such problems and I'm not blessed with a ton of spared parts to swap out to try to ferret out a hardware issue (though if push comes to shove, I can gut my system and try swapping out parts, but I'm hoping for a simpler solution). I'd appreciate any advice / suggestions! The system specs are as follows:

AMD Athlon 64 2800+ (retail package)
Asus K8N motherboard, BIOS rev. 1009
1GB PC 3200 (PNY branded)
PowerColor (ATI) Radeon 9600 Pro 256Mb (8X AGP)
Western Digital 80GB SATA HDD (WD800JD)
Pioneer DVR-110DBK (DVD recorder)
Antec SLK1650B 350W (case/power supply)
Windows XP Pro (SP1) - cannot upgrade to SP2 as of yet - no internet availbale to this system

 

One stick of RAM.

 

I do have another stick of PC3200 (512MB) that I will try if push comes to shove. I may have been a bit hasty in my posting this thread - I'm still monkeying around in the BIOS to try to see if there's something wrong in there. The only thing I can remember changing from yesterday is that I disabled the useless "instant music" feature (allowing cd's to play without powering on the system). Since then, I haven't been able to replicate the boot-up failure in about 25 restarts (both software and power switch induced) - yesterday I experienced lock-up in 2 out of 5 starts. So for now, I have my kids on alert to let me know if they have any problems. If the issue springs up again, I'm going to start with swapping out the RAM, followed by the video card (since the failed boots do not produce a video image). The power supply doesn't seem to be the issue (everything seems to get juice), but I caould always move there next. Anyway, thanks for the help. If you have any last minute suggestions and/or diagnostics I'd appreciate it (e.g., if it turns out to be a RAM issue, does that mean that the RAM is simply incompatible, or bad, or is it impossible to determine?). Otherwise, I'm going to leave this thread idle until I hit the next SNAFU. Thanks again.