XPS 8300 4 rapid beeps

I put the Dell XPS 8300 (circa 2012) to sleep and left it for a few days. When I returned, the CPU and case fans were spinning up, then immediately turning off, then spinning again. 

After reading several posts here and elsewhere, I removed all internal components, replacing one by one. I tested the power switch. Nope.

I then replaced the power supply with a newer one (600w vs. 450) - same symptom. 

Next, I replaced the motherboard and - viola! The system purrs and is making those sweet spin-up noises, but there are 4 fast beeps and a flashing amber power switch. There is no display on the monitor - I've tried using both internal video and external video card. 

Research shows that 4 beeps means a RAM issue. I removed and replaced 4 sticks, one by one. No. Next , I tested the modules in an almost identical computer - they all work fine.

I also replaced the CMOS battery.

One poster wrote that he forgot to install the offsets when he **bleep** in the motherboard, causing a short. I was certain that the offsets are built into this case, but I removed the MB just to double - check. They are, and there were no stray screws anywhere.

What is left? Could it be the CPU? Seems unlikely to me as the original symptom went away with the new MB. What am I missing?

I'd sure appreciate any advice that may be offered!