In your position I would use another oscilloscope, or even the working channel of your faulty DSO to look at the signal path in the faulty channel. Check at its output that feeds the ADC and see if a correct waveform is present there. If not, work your way back towards the BNC input connector checking where the signal is failing to make it through a component correctly. I suspect a power rail issue as you appear to be losing half of the waveform, but there are other causes of such a fault.
With two channels available on a DSO and only one that is showing a fault, there are options to use another oscilloscope to compare signals and voltages so the lack of a schematic diagram is not so serious a problem. You will be well served to dismantle the DSO, photograph the PCB with decent resolution and identify the IC’s used in the channel input stages. The data sheets for the IC’s will help you to choose suitable points to monitor for the injected test signal. If you upload the PCB pictures here, members of this forum may be able to assist with suggestions for test points etc.
If the signal coming out of the ‘faulty’ Channel and feeding into the ADC stage is correct, you will need to look at the power supplies to the ADC and hope that it is something simple like that.
Fraser