Mid-2011 MacBook Air with three beeps and constant restarting

Hey guys, I've got a mid-2011 13" MBA that I've owned since new. It's been an absolute champ, and now I primarily use it as a backup. A few days back, after having not used it for a while, it was on the charger in my office and started the constant three beep issue. I've tried the SMC reset, as well as the PRAM reset, but the issue persists. When it does finally boot up, it freezes after loading the desktop and then restarts. Interestingly, if I boot in safe mode, it seems to run fine and does not enter the restart loop.

Any ideas? It's looking more and more like RAM, which I understand to be made on the logic board in this model, but I'm open to any ideas/suggestions! Thanks!