Does the fan for the condenser unit start?

No.

CY: Unlikely to lose the comp and the fan both. Maybe bad relay.

Did he measure the voltage at the leads going to the compressor?

Yes

CY: And got what results?

Why did he bypass the relay
(contactor)? Was it not latching up?

Even if the relay latches, the points could be burned, preventing contact.

CY: That's true. How about the power safety disconnect? Working properly?
Sometimes those corrode.

I know these are fundamental
checks, but you would be surprised at how some pros diagnose a unit.

Well, the first thing he did was test the start capacitor and pronounced it
"marginal." So he replaced it. No joy. That's when he went through the "try
this, test that" mode.

CY: Amp draw check is important. Also continuity across the compressor
terminals.