Input problems are not uncommon on Q*bert boards. You probably have an issue on the down/right input line. If you trace it into the PCB from the edge connector, you will see that the line is connected to a few resistors, a capacitor, and ultimately a logic chip. (I don't have my schematics handy to tell you which chip it is.) The way it works is the input line is at one voltage, and then changes to another voltage (usually ground) when you close the switch attached to that line. If your non switched voltage is at the wrong level, the chip may think the switch is always closed. The chip monitors a number of the inputs simultaneously, but it is possible to have one 'leg' on the chip burned out. I have also seen bad capacitors and resistors on input lines, which give you the wrong voltage. Input lines are pretty prone to damage, as things like shorts or static discharges can do a number on the components attached to them.
...so I would get out a multimeter and start measuring those components. When you get back to the appropriate leg on the logic chip (that corresponds to down/right), check and see (with the machine turned on) if the voltage on that leg is the same as a leg corresponding to a direction that is working correctly, i.e. up/left or one of the player start buttons. If the voltage is different, i.e. always low, the logic chip may be working and one of your passive components (a resistor pack, single resistor, or capacitor) may be blown. Even if the voltage is off due to bad passive components, the chip still *could* be bad though.
Of course, you could have something further on up the chain that is causing this problem, but my money is on the input portion of the circuit. I hope this helped a bit.