Sounds as though it's failing the power-on self test (POST).
Or perhaps one of the peripherals is drawing too much power. Disconnect all peripherals.
If you keep having trouble you may end up having to disconnect a few internal items. Such as modem, network card, wireless card, and remove all but one RAM chip.
Just as it's starting up, can you press the right key that opens the BIOS settings?
Look for things like RAM memory testing, etc. A bad memory IC can halt startup. I don't know if all computers display the progress while testing RAM. It might help to have this on, in case you can spot something looking wrong.
Or, you can try turning off RAM testing.
If the hard disk is bad, then more time will probably go by before you see an error message about the disk.
Consider starting from a boot CD.