XPS 8500 won't boot

I have had my Dell 8500 since 2012 and I have not had any problems with it, until this week. I heard the machine making a noise like it was waking up from standby mode. The fans start, but only run for about 1 second, then they stop. This cycle repeats about every 4-5 seconds. There is nothing on the screen, and there is no evidence the BIOS POST is running. I do notice that the power LED on the back of the machine goes out when the fans start and comes backs on when the fans shut off.

I've disconnected everything but the keyboard and monitor, and that does not change the symptoms. I removed all the memory except for one DIMM in slot 1 and that did not help. I rotated all the memory DIMMs, one at a time, into slot 1 and that did not change the symptoms.

I suspect the power supply or the motherboard. Has anyone seen this behavior on an XPS 8500? If so, were you able to resolve the problem, and what did you do?