T5500 diagnostic lights 3 & 4

It does sound as though it's probably the motherboard.

Is it just a single CPU configuration you have? If it is, you could try them, one at a time, in slot 2. If it's a dual CPU, try removing the riser and testing the DIMMs in slot 1 again. 

If you try with no DIMMs at all, do you get just the 1 LED lit? (indicates no memory detected)

You could also try removing the mains power and disconnecting the CMOS battery, hold in the power button for a few seconds to drain any residual power then reconnect and test again.

Other than that, all you can try is to remove all other components apart from the CPU, power switch and PSU and test again. If you get the same symptoms it's highly likely to be the motherboard.

Let us know how you get on.

It's a dual CPU with 3 memory modules (4GB) on the motherboard, 3 on the riser. I have removed and replaced the CMOS battery and it has gone into Pre-boot System Assessment Build 4527 (with diagnostic lights 1, 2 & 3 permanently lit) and currently still running memory tests (5% complete as of now)

Memory test completed, theoretically passed. Still getting the same 3 & 4 sequence. I have removed and re-seated all 6 memory modules, replaced the CMOS battery and followed the reset procedure using the jumper pins.

No progress. More detailed observation of the boot process shows 1 & 2 flash on and off in sequence as normal, at the same time 3 & 4 flash three times together then stay on. After about fifteen seconds the system reboots and repeats. On pulling the power plug the power switch flashes amber and 1 & 3 flash in concert fifteen times before stopping.

With all the troubleshooting you have done, if it's still giving the same indicators with the 2nd CPU riser removed, it's going to be the motherboard at fault I'm afraid.

I feared as much. While I am quite happy to replace/install various components, I certainly don't have the expertise to replace the MB myself and feel more inclined to get a whole new box as the quickest solution (I am making do with an older machine and software) and sell this one for parts/repair.

Here's the service manual:

http://downloads.dell.com/manuals/common/precision-t5500_setup%20guide_en-us.pdf

Take a look, it's probably easier than you think!

I have found a T5500 MB on eBay but it has PN D883F, whereas the one in my machine is CRH6C - is the D883F compatible?

D883F should be fine. It is listed as a substitute part for CRH6C (meaning it was to be used for warranty repairs in the event that  CRH6C wasn't in stock)

Your problem will be solved if you've been recorded correct bios

For anyone who comes across this thread while searching Bing, Google, etc...

The problem may not be just the motherboard (e.g. MOSFET), but the processor may also be fried.

I had an identical sequence of codes with a dual processor T5610.  I found the shorted MOSFET on the motherboard, but upon swapping the 2nd processor into CPU1 socket (to test it), I discovered the 2nd processor had also been destroyed when the CPU2 side of the board went down due to the above mentioned MOSFET.

Amazingly, as long as the 8-pin power is disconnected from CPU2 and the slot is empty, the machine will work!  The system is only working on 'half a brain'... it's not ideal, but the system is running fine on CPU1.

I'm not sure if this will work in a situation where the CPU1 side of the motherboard is the problem.  ???