Wellcome on the forum.
Security advise : the CRT of an analog oscilloscope works with high voltages , this can be lethal, you try to repair it at your own risk.
If you are aware that you have not enough knowledge and experience for working with high voltage, ask for help to somebody who knows.
The first thing to do is always a visual inspection: look for burned or broken components, bad solders, bulged or with leakage capacitors, loose connectors or wires, cracked boards,
After this, check all the power supplies .