Although it is more common for the resistors to cause the digits to stop working, the drive transistors can also fail, giving the same fault.
If replacing the resistors doesn't fix the non-working digit, then the following transistors will need to be replaced:
2N5401 - Digit Drive Transistors
Q7 - 1's Digit
Q8 - 10's Digit
Q9 - 100's Digit
Q10 - 1000's Digit
Q11 - 10,000's Digit
Q12 - 100,000's Digit
Q21 - 1,000,000's Digit (7 digit display only)
MPS-A42 - Level Shift Transistors
Q1 - 1's Digit
Q2 - 10's Digit
Q3 - 100's Digit
Q4 - 1000's Digit
Q5 - 10,000's Digit
Q6 - 100,000's Digit
Q20 - 1,000,000's Digit (7 digit display only)
Either the 2N5401 or MPS-A42 transistors can cause a non-working digit, so best to replace both for each non-working digit.