What you're describing sounds a lot like part 4 of the "Pyramids of Mars", except that I don't think there are any chessboards. "The Five Doctors" has a chessboard, so maybe that's the one you're looking for, though it seems like the two stories could have merged in your memories. The other tip would be "The Hand of Fear" AKA Eldrad must live, as the last part has the doctor going through a series of traps.
I'm sorry about your uncle and I'm hoping that you'll find what you're looking for. I'm planning to watch all of the old stories again sometime soon, so I'll keep an eye out for the things you described and I'll let you know if I find a better match.
"Once, I was a real turtle"