Is the warranty still active? If so call Dell at this point FOR SURE
WHEN the issue is happening I'd disconnect everything that isn't needed & try to power-on again. Have only the PSU connected to motherboard, CPU, 1x RAM stick. Disconnect: all external connections except for power cord, hard drives, PCIe/expansion cards, front panels, case fans, etc.
Have you tried a power discharge? Disconnect power cord, hold power button for 30sec, reconnect power cord. It's fixed something like this on a laptop for me
Have you tried to reset CMOS via this RTCRST (Real-Time Clock ReSeT) jumper? I know you mentioned the battery, but this way is usually better.
You did AWESOME process-of-elimination, however because of the complexity of doing this over time I DO honestly think you might have assumed on some things so I'd try to repeat those steps. Nothing against you, I've been in your situation. When I exhausted my ideas I revisited things only to discover I mis-remembered or assumed some things. Problems can be intermittent too making things all the more difficult :(
Front panel LED's 3 & 4 indicate (per owner's manual pg51):
Memory modules are detected, but a memory power failure has occurred.
- If two or more memory modules are installed, remove the modules, then reinstall one module and re-start the computer. If the computer starts normally, continue to install additional memory modules (one at a time) until you have identified a faulty module or reinstalled all modules without error. If only one memory 51 module is installed, try moving it to a different DIMM connector and re-start the computer.
- If available, install verified working memory of the same type into your computer
Another Dell resource for blink/number codes. Dell article on supported memory for this PC model (2nd one)
- Hopefully you have a newer BIOS? A11 fixed a number of issues, A16 fixed a 'Intel Reboot issue' related to a security CVE
- Have you reviewed all the Dell articles about this model? I was trying to skim them for you, but I'm too busy