Macbook display randomly garbles. Corrects for a while when I plug in an external monitor. What's up?

I have a late 2011 Macbook Pro that has some random display issues.

1. The laptop display will put a 1-inch black bar down the screen and shift everything to the right. It fixes itself for a while when I plug an external monitor into the mini-display port, but then does the black bar thing again.

2. Screen just totally garbles and I have to do a hard restart. Plugging in the external monitor seems to correct this for a while, too.....

I went into System Settings and unchecked the box so that it would only use the discrete graphics, and it doesn't help.

Failing GPU? Discrete or on-board? I'm guessing failing discrete GPU......

Thanks for any help!

Joe