TBH it all smacks of either faulty RAM or faulty connectors. What I would do is memory diagnostic when laptop boots (Memtest X86, GoldMemory etc. - but bootable solution) and see if everything is ok. If RAM module(s?) is 100% ok, there may be something else like:
* RAM incompatibility or partial incompatibility (can be solved with BIOS update/reset sometimes)
* Damaged RAM pins or RAM socket pins (if you have multiple, it may be only one of them)
* Layered dust on connectors or some other gunk (wipe them gently with soft non static fabric and rubbing alcohol)
Check for these problems and try fixing, and see if it you get any better clue on what might be an issue.