Q: Macbook 3 Beeps on Startup (and more)

Friends, 

I've been having a lot of trouble with my mac starting a few months ago.  I first noticed the problem when I would grab my Macbook Pro by the top-left hand corner of the base (grabbing by the esc key). 

After I would grab it, the computer would immediately restart.  This wasn't a huge problem, until my laptop began beeping 3 times upon startup.  Ultimately, I figured this was a RAM situation, and it just needed to be re-seated.  This would be my go-to fix if the beeps ever started up again (which they would every week or so).  My problem has gotten worse and worse, and the beeps come back sooner and sooner.  I'm constantly worried the hard shut-downs are eating away at my computer, and I don't know what to do.  Every now and then, the screen will have bars going across it, as well, upon grabbing the upper left-hand corner. 

Any help is appreciated, I plan to take it in as soon as i get home (I'm a college student) but want to see if there is anything I can do.  PRAM has been reset, and all RAM were pre-installed. 

I'm working with a MacBook Pro (13-inch, Mid 2012) and running El Capitan.  8 GB 1600 MHz DDR3 RAM that both say 'OK' in diagnostics.

Thanks so much guys, let me know if I can provide further information.