As nctnico said, remove and carefully inspect the front panel board.
On my TDS520, the Shift button was not working correctly. I pulled the front panel off, pulled off the membrane switch pad and cleaned the contacts. It
didn't occur to me at the time to actually look at the bottom side of the board where all the components are. Had I looked I would have several puddles
of wet electrolyte. Needless to say, my button "fix" didn't last more than a day. It probably only worked for a short time because all the manipulations
moved the puddles around.
Assuming any damage is not severe, the board is easily re-capped (there is plenty of clearance for normal radial caps). Simply twist off the old SMT caps
gently with a needlenose, clean, clean, clean and clean again, then tack on the leads of a normal cap (or use SMTs if you must).
If it still doesn't work, then you can start fiddling with the encoder. And, by the way, if you do replace the entire front panel assembly, that needs to be
checked for bad caps also.
And just to spoil the rest of your day - when you open it up, you should inspect ALL of the boards.