When asked to solve a puzzle in an interview, talk through the process of solving the problem so that the interviewer can see how you think and what you will do when you come up against a part of the puzzle you may not be able to solve.
Is there power getting to the scope?
Is the fuse open? Check with DMM.
Can you hear the scope turn on and start up?
Some scopes have a brightness control. Has that control been turned down?
Pressing the on button, but there is no evidence of the scope coming on. Fuse is good. Power is good. Most likely something internal at this point.
Do you have a warranty? Yes, send it in. No, check it out.
Open the case, and check the on switch. I have known those to potentially go bad.
Can I see anything visibly wrong with the scope inside?
Online resources available? Schematics, forums, advice, drawings?
Do my employers want me to continue using man hours working on getting this fixed or would it be cheaper at this point to just get a new scope?
Find a new scope to complete the job that needs done for the time being.
It’s time to make a decision at this point on what the best option moving forward would be.