Help Dell Dimension 9200 cycling on/off every few seconds

I have an old Dimension 9200. I replaced the power supply with a good one about a year ago (Corsair CS600)

Today the computer stopped booting. When turned on, the power button goes to green. Diagnostic lights 1,3,4 go on, then 1 goes off, leaving 3,4 on. The hard drive spins up for a second. Then the computer shuts off and tries to reboot. It does this in an endless cycle.

Lights 3,4 indicate a bad memory module. I have 2 pairs of DIMMs. I tried cycling them in every combination I can think of, but the same thing happens. I tried removing all the memory, and light 1 came on and stayed on (as I would expect)

I tried unplugging, holding power for 15 secs, removing the battery, holding power for 30 secs, and reinstalling battery (I assume this clears the CMOS?). Didn't help.

I'm thinking about purchasing new DIMMs, but I have a funny feeling it's not really the memory. Before I did that, I wanted to see if anyone on this board could suggest something else?