Incredible! These instructions (as well as a video by Mike Gomez following these directions) helped solved this!

I did not order a new connector board. Simply removing the connector board and putting it back in place solved this issue. I did not do anything special with the connector board once it was out. I looked around for things like dust and lint, removed nothing, then placed it back. I'm not certain how long this fix will last, but I'm sure it bought me some time.