Unless I'm missing something, it sounds like you've narrowed it down to a board issue. So just to double check you removed the row and column connectors and jumpered row1 to column1, row 1 to column 8 and row 2 to column 8 (using a diode in all cases) and switch 21 also indicated closed? If that's correct then continue reading.
Next question is if the problem is in the row or column. Check all of the column voltages at the CPU. This is a pulsed signal and if one is locked on, which could be causing your problem, it will have a higher voltage reading (specifically column 2).
You could also close the following switches and see what happens: 16, 17 and 27. If switch 26 also indicates closed you've got a column problem.
To check for a row problem close switches 51, 58 and 68. If 61 shows closed you've got a row problem.