post is basically what occures before video is initialized.... tests everything, with no cpu, nothing can be tested, so cpu is the first thing to test....
post works fine (to some extent) with no memory, (motheroboards still have that 640k base memory iirc). i have confirmed numerous times that without memory i get a post no problem, 3 beeps depending on brand of bios...
with voltages screwed up (under or over powered) it is possible for post to fail, i have seen it happen but it is rare, simply change the psu with a known good one or use a voltage meter to check for red = 5v yellow = 12v, and orange = 3.3v (is it orange? i think it is, too tired) all withen about 10% (or sometihng like that) in either direction.... consumer motherboards dont really care (they do but not enough to demand ripple be under X threshold) about ripple from the power supply (dc power almost acting like ac, bad filter caps)
i have seen some wierd occurances before also, stuff shorted out, like incorrect floppy cable (not backwards, but offcenter) has fried some stuff, also sometimes if you have certain pci cards in it will fool around with the post/ other stuff... (mainly controllers and vid cards)....
in some cases ram is required to post, either it being good or bad,,,
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to summerize my rambling nonsence:
no post: bad cpu, motherboard, short somewhere (check for debris on mobo), corrupted bios, memory (sometimes), and psu... thos are the main ones i have seen as i have been working repairing computers for a very long time...
it is a general rule of thumb to use process of elimation.... eliminate everything possible, disconnect all drives, cards, and stuff (INCLUDING POWER TO DRIVES)... so you have atx power, (and 12v, i have seen no post because the 4 or 8pin 12v wasnt connected), speaker connected if not onboard, (not the audio jack one, rofl)... and power/reset, power led if you wish... and obiously the cpu, and ram... (try to get known good ram, or use 1 stick... also use bankA slot 0 first if you can (basically closest one to cpu))
hope it helps, now ima go pass out on my bed