Mid-2012 Macbook Pro displays multicolored columns on screen, crashes, three beeps (5 second pause in between)

I have a 13" mid-2012 Macbook Pro (non-Retina version) that's been crashing consistently as of late. Prior to shutting down, it displays columns of red, green and blue on the screen (see image) and the screen goes black, accompanied by beeps occurring in sets of three (with 5 seconds in between). My Macbook has suffered from this problem before, and I've had to unscrew the bottom plate, take out the RAM chips and put them back in just to get my Macbook to power on again. Having learned from Mac support that this pattern of beeping corresponds to a RAM problem, I took a chance on purchasing two new RAM chips (2x 4GB, an upgrade from the 2x 2GB I had previously). I'm still having the crashing/three beeps problem, I just don't need to take out the RAM chips anymore to get my Macbook to turn on again unlike before. What could be wrong?