I agree with Sceadwain, try it in the XY mode. This will prove whether the X amp is working. If you don't have a signal generator, take the signal from the secondary of a mains transformer. eg. 6 V AC.
I have had to repair my HP scope many times as it is old and resistors tend to go high resistance.
However, I have the service manual, which makes it easier.
Since you don't have this, I suggest that you do a visual inspection and look for any dry joints, burnt components, etc. You could also measure the resistance of the resistors with a meter. Remember that there may be parallel paths that will affect the reading. However, if it is higher than what the colour code shows, then it must be faulty.
If the reading is lower than expected, reverse the leads as there may be a parallel path through a semiconductor.
Also measure the voltage at various points including the supply rails.
You can also trace out the circuit in the area where the fault is. It is tedious and time consuming.
But the fault is likely to be some thing simple such as a dry joint or a faulty component. So it would be a pity throw the scope out if you can spare the time.