[bagofcrap24]

Any chance that your sd card is a current Samsung one?
I've had huge problems with a brand new 16 GB Samsung Evo on my RPi2 - even without overclock and using 4 different chargers (10A multi-charger with high current port, 2A samsung charger, 1.2A charger from amazon, 1.5A charger from samsung) I encounter system corruption every 2 to 3 boots.
After switching to a 64GB sandisk ultra micro sd I've used in my phone previously all my problems are gone.
I think there has been some acknowledgement on the official boards that current Samsung cards might cause problems, although the can't reliably reproduce it yet.
Not sure if that's related but I'd try different (old) cards if you have problems booting your RPi using new cards.

This is the one I first tried. I got OpenELEC to work, but I have this small colored square in the upper right hand corner. Not sure what it's from.

The small rainbow square is an indicator to say that your pi is not getting enough current. Try with a better charger.
I have a b+ and a pi2 both using 16gb Samsung evo cards running at 1ghz without issues. (They are cron jobbed to reboot every night)
Maybe I'm just lucky but I've seen no such corruption issues using the Samsung cards.