Increased RAM usage shouldn't be an indicator of a problem.
RAM is a solid state device, there are no moving parts, so RAM either works or it doesn't work at all.
Depending on the brand or quality of your motherboard, heat could have been a factor.
You say that is happened after you moved.
When you stored computer during move did it sit in places with a lot of heat?
Circuit boards on the motherboard could have been damaged from high heat if so.
If you have access to another computer, I would try swapping out each component of the "broke" pc with the working one, until the working one exhibits the same behavior. (including the power supply).
The following are the parts that could fail that could cause graphical glitches (From worst to least)
Graphics card (either damaged or improperly seated)
CPU
RAM
Power Supply (Not providing enough or constant power can cause issues)
Extra slot cards (additional sound card, SSD drives) Usually them not being seated properly can cause issues
Cooling system (not keeping system cool enough) ** Esp. consider this if issue doesn't happen right away. **
If you have swapped out everything but the motherboard, and still haven't seen the issue, then chances are it is the motherboard.
If you are not comfortable with swapping out parts or do not have access to another PC with similar parts, I think it might be time to take it to a PC tech.