The display had totally gone goofy. Pixels would be looking like white noise.

I tested the ribbon cable with a multimeter and found most of the leads with high resistance. After removing the bad ribbon cable and cleaning the solder points, I found soldering at this small scale to be far too tricky. Instead, I found conductive glue at RadioShack. Now all I had to do was bridge the gap with scotch tape and make my glue trails.

All fixed!