If it works fine in safe mode, then it is NOT the RAM. Memory failure would be evident no matter WHAT was going on. Safe mode, in the BIOS, Linux, whatever you want to run, if the memory was bad it wouldn't make a difference.
It's more likely you have a failing graphics adapter or panel if the visual problems are what is happening. That would definitely be affected by being in safe mode because in safe mode only minimal graphics drivers, not the full graphics driver package, are loaded and used.
Very doubtful it has anything to do with your memory at all as far as that part goes. I don't know what the issue is this early on, but it's pretty doubtful that it's memory and running in safe mode is not a fix. Fixing the problem, is a fix. And fixing the problem might mean replacing the unit if the problem is a faulty graphics adapter, or motherboard.
Very possible that it's a bad motherboard as well because that could cause graphical corruption like you are seeing AND memory errors.