My first thoughts:
https://www.dell.com/support/kbdoc/en-us/000127927/a-reference-guide-for-latitude-notebook-and-tablet-diagnostic-indicators
Have you tried reseating the ram and swapping out modules one at a time?
Bad ram is so often the culprit.
Removing one module at a time, trying only one module, and then swapping them around after reseating them
might fix the issue or at least change your LED indicators.
Have you checked all your internal component connections yet (hdd, videocard, modem, CPU, ODD, etc.)?
It's remotely possible you might need to replace the cooling paste on your CPU after so many years.
If it's cheap and easy, I would replace the BIOS battery just for good measure.
Good luck!