RAM DIMMS can have varying degress of faults and there are specific tools that can test for these over periods of days. Basically there are loads of different tests to stress the different types of loads put on DIMMS, but you're correct in that the fault should show pretty quick if it is the memory.
To test for dry joints requires specialist knowledge / electrical training which was the point where I stopped. Take it to a shop unless you have the appropriate knowledge / scopes etc. And theory is that the problem will get worse with time, and eventually total failure.
If you have an electrical meter you could test for voltage from the PSU lines - BE CAREFUL IF YOU DON'T KNOW WHAT YOU'RE DOIN HERE FOR OBVIOUS REASONS
- to prove that voltage is getting into the unit. If you are getting voltage then given you've tried all the other major components, I have to guess that it's PCB / dry joint / PCB component failure. I'll try & route out the voltage thresholds for you.