https://www.dell.com/support/article/us/en/04/sln288973/power-and-diagnostic-led-configuration-status-for-the-precision-workstation-t3610-t5610-t7610-systems?lang=en 

Did you every figure this out? I have a T7610 with the same problem. I put the power supply into a T7600 and it works fine.

I have the exact same problem with a T5610 dual processor setup, except the problem goes away if I -unplug- the 8-pin cpu2 power cable and remove cpu2.   With only cpu1 installed, the system works fine.  If it merely plug in the cpu2 power connector itself, the PSU will click and halt, with Power Button + 1 & 3 diagnostic LED's all blinking.

Tried a different (known to be good) PSU and the problem persists.  CPU2 power cable tests good, as does PSU.

Regarding my dual-processor T5610 mentioned in previous post (similar problem as T7610 above):

I finally got around to testing the motherboard at the component level. All the MOSFETs for powering CPU2 were blown (shorted internally) so they weren't switching on/off. Amazingly, the system still runs on CPU1.

My choices are:

1) Leave it alone and run the system with a single processor (CPU1)
2) Attempt to replace all the CPU2 MOSFETS with my rookie skills (could ruin the board)
3) Buy a replacement motherboard 

I'll probably wait for awhile and do #3 when I find a used board on eBay at a good price.

Same problem, started a last week, Now I Have to pull the power plug out and wait a few minutes before plugin it back. Than it starts up.

After that the Machine works all day... But I have to unplug it ever-morning to get it past POST.

I was going to buy a new coin cell battery today but after reading your post I'm not sure that it will help.

Do you still have the problem? Or have you fixed it?

Hi Allanchanly,
 
My problem is fixed! I pulled every external cable out and put the machine on my bench for a visual inspection. I noticed that the GPU connectors in the back were very close to the chassis which meant that the monitor cables could not be pushed in all the way and that the outer shielding of the cable connectors maybe touching the chassis when plugged in.
 
I insulated the chassis from the monitor cable(folded business card) and plugged them into the GPU. Now the outside shield of the cables are touching paper and not the chassis. Powered on and it all worked.
 
Not sure why this is an issue as the chassis must be earthed and the cable shielding likewise, But I have to assume that their must be some kind of earth leakage detected on POST.

To follow-up on my previous post, I followed the instructions I found in other pots to test the power supply by pressing the button on the back near the line cord. That indicated that the supply was good, which wasn’t surprising since it worked in another workstation. As suggested below, I removed processor 2 (there is no 8-pin power connector specifically for CPU 2 on a precision T7610), and the system would then boot normally. To test if it was the processor, I put the 2nd processor into the socket for CPU 1, and it also worked. As a result, I bought a used motherboard on eBay. It wasn’t all that hard to replace, though it did take a couple hours. The system now works. I suspect that there must be a problem with the on-board power supply circuitry. However, there aren’t any components that are obviously damaged, and I don’t have the expertise or time to try to figure out what is wrong. It is worth the $150 I paid for the motherboard to get the system working again.

I have the same problem, but in this case I have the orange light 1 2 and 3 on and the monitor does not give me video, I need to know what the problem is, I already replace the RAM.

The 1,2,3 error code gives a vague description.  Please see below.

Granted it's not a connection problem, try replacing the size 2032 CMOS battery.  If that doesn't work, then try a BIOS reset via the blue jumper on the MB.

One of 2 things could happen after replacing the battery:  1. It works.  2. It gives an error code that isn't so vague.  I've had experience with pc's changing error codes after replacing the battery.  Bad batteries affect BIOS and therefore pc operation.

Some other failure has occurred.

Ensure that the display/monitor is plugged into a discrete graphic card. Ensure that all hard drives and optical-drive cables are properly connected to the system board. If there is an error message on the screen identifying a problem with a device (such as the floppy drive or hard drive), check the device to make sure it is functioning properly. If the operating system is attempting to boot from a device (such as the floppy drive or optical drive), check system setup to ensure the boot sequence is correct for the devices installed on your computer.