Is pin 10 on U6 going to 0 V when you press one of the non-working keys? If so, then yes, U6 seems to be the problem. It’s not responding to input on pin 10 as it should.
As you see in the schematic, ‘Ctrl’ through ‘J’ make up one row of the keyboard matrix. The fact that all the other keys are working indicates that most of the circuitry is working, and the problem is restricted to just that row.
So what’s attached to that row? Pin 10 of U6, pin 10 of RX2, pin 17 of U4, and the traces and solder joints in between. The objective, then, is to isolate which is going wrong.
Your continuity check indicates that the traces and joints are fine. Having 5 V on the row when powered tells us that the pull-up resistor in RX2 is working (and it’s unlikely to fail anyway). That leaves U6 and U4.
U6 is a NAND gate with all of its inputs normally pulled high and its output low. Pressing a key should take one of the inputs low and cause the input to go high, triggering the startup of the microcontroller and strobing of the column lines (thus causing pulses to appear on the row line, not just a steady state).
If, when you press the ‘A’ key, you see a steady low on pin 10 of U6, that means the microcontroller isn’t walking through the column lines and probably isn’t on at all. Seeing a steady low on the output (pin 13) of U6 shows that it isn’t responding to the input properly and starting the microcontroller. If it were a steady high, that would be the right output (for a steady low input) but raise the mystery of the lack of column probing by the microcontroller. If you saw pulses on pin 10 and pin 13, that would indicate that U6 worked and triggered the operation of the microcontroller (U4), but U4 wasn’t reading pin 17 correctly.
The TI CD4068BE should work as a replacement.
Mouser,
Digi-Key,
Jameco