PC posts only if warmed up (?)

This is not related to Windows 7 but i did not know where else to post. It's about my older PC that still runs XP. I hope this is not a problem. Please help me. I think it is more of a hardware problem.

The PC is about 10 years old. Here is the current config:
Compaq Presario 3600AP
P4 1.5 GHz Socket 478
256MB SDRAM in 2 sticks 133MHz
ABIT BL30G mobo
XFX GF 4 MX 4000 128MB
20GB IDE on primary
120GB SATA with SATA-IDE adapter on secondary IDE

PC was being used till a month ago. No recent hardware changes, but PC was packed and moved a month ago and was started only a day ago. When i start it, monitor light goes orange with no display. No POST, no beeps. Power light comes on, CPU fan spins, molex fans ok, HDDs spin up. Power button needs to be kept pressed to turn off.

Now if i leave it on in this pre-POST state for about 5-10 minutes, then turn off by pressing power switch as mentioned above, and then turn it on again, it passes POST, and proceeds to boot. The (Safe mode, SM wit CP, SM with N, Last good config) menu comes up. I choose start normally. Before a second passes on the Win Xp boot screen it hangs. Trying safe mode it hangs at "agp440.sys".

The insides are cleaned atleast once a year and was last cleaned about 3 days ago, less thoroughly than the yearly cleaning. The PC has a problem of draining the CR2032 within a week or 2 if not used that period.

I will continue my troubleshooting, and post my observations, but in the mean time please help with any suggestions, or ideas as to what is wrong.

What could be causing the need for the "warm up" period?

Is it possible that the graphics card has failed? Could the agp440 and the warm up be linked? Basically im asking if hardware can cause the hang at agp440.sys.

Will try the HDD on this PC (My system spec), and older 16MB video card on the problem PC and post results.