I have found that the NiMh cell is a common fault on these plug in time switches. Sometimes they do not hold a charge and somtimes they seem to go open circuit so that when they are plugged in the charging current raises the voltage abobe the normal battery voltage and this causes allthe segments of the display to be dark. Does the time display increment normally ? If it does then the crystal is OK.
The actual timer part is under a black blob of resin on the board with the display. The board in your picture is just the relay driver and charging circuit.
Les.