Weird memory issue

[Kendric Beachey]

I just got four 2GB memory modules for my computer (running on 1 GB
was starting to try my patience).  These were destined for the four
slots on my motherboard (Intel DG965RY).

These combinations produce a happily working machine:

any one DIMM in any slot
any two DIMMs in any two slots
any three DIMMs in any three slots

This combination produces a machine that can't get as far as the BIOS
power-on self test:

all four DIMMs in all four slots

It fires up the fans and stuff for about five seconds, then shuts off.
 Then it waits about five seconds, and fires up again...and it repeats
the cycle, endlessly, until I pull the plug.

Has anyone seen this sort of thing before?  All of the DIMMs and all
of the slots have been proven to work in isolation or combinations up
to three...it's just when I try to use all four at once that it conks
out.

Kendric Beachey