Since you have identified the problem as a board fault, I would check these resistor parts first. Pretty common for them to have issues that play havoc on the matrix scanning.

SR9/SR10* = 1k ohms x 4 resistors isolated/discrete (8 pins). Used for the switch returns (rows). Mouser part# 652-4608X-102-1K. Easy to test in-circuit.
SR11* = 560 ohm x 9 resistors bussed (10 pins). Used for the switch returns (rows). Mouser part# 652-4310R-101-560. Easy to test in-circuit.
SR3/SR15/SR17* = 4.7k ohms x 9 resistors bussed (10 pins). Used for the switch drives (columns). Mouser part# 652-4310R-101-472.
SRC6* (1k/470 pfd) = resistor/capacitor network for switch matrix columns. Has 1k ohm resistors with 470 pF caps in a single package. Can not be tested in-circuit. Replace with a 1k ohm x 9 resistor bussed (10 pins) with no capacitors. Cut off pin 10 (important!), and install pin 1 (common) in pin 1 of the board. The cut pin 10 of the resistor network does not go into the board's pin 10 position. See notes below for more info on this. Mouser part# 652-4610X-1LF-1K.

Where the test guides indicate the pack is "easy to test in circuit" means that other components in the circuit either do not affect the measurement or affect it very little. Some of these resistor packs should measure the designated value without physically desoldering or removing them from the circuit.

Find the common pin, designated by a dot or notch at one end of the device. Set your meter to ohms and measure from this pin to each of the other pins in turn. As an example, SR11 should measure close to 560 ohms from each individual pin to the common pin. Measuring 580 ohms on one of the pins would be an example of close, and over 1000 ohms would be an example of not close. If you get one that is way off, desolder it from the circuit and check it again with a meter. If it is out of spec, replace it.