I got a look at the cable tonight. Both ends were undamaged and didn't look corroded at all.
I took a look inside the socket on the Blu-ray drive though. The socket had many pins in there but on the end one of the pins was more flattened into the back of the connector than the others.
I put a single piece of scotch tape on the blue side of the Blu-ray ribbon and trimmed the edge with a razor so it wasn't any wider. The tape seemed to give the cable enough thickness to make contact with the more flattened connector pins on the side of the socket.
My PS3 is accepting, ejecting and turning on with discs again!
Thanks for the help!