When installing RAM:
- unplug the system from the wall (if a laptop, remove the battery also)
- grab the metal chassis of the case (to discharge any static) and continue to hold onto it.
- undo the clips and remove the memory modules.
Then
- take the new memory modules and place them in the slots.
- seat them with one hand (if possible) so you can keep the other hand on the case (so static won't damage it).
- if not possible, use both hands as quickly as possible - and don't move around a lot (to prevent more static from building up).
After that, run MemTest 86+ (I find the other tests are less reliable) according to the instructions here:
Link Removed - Invalid URL
You can also run Prime95 to stress test the memory (the Blend test is the most torturous on RAM) - link to it is here:
Additional Hardware Diagnostics
You must fix the RAM problems before investigating any other problems. Let us know if the new RAM fixes things and we'll move on from there.