Volvo won't start - but not always

Volvo doesn’t turn over at all. Lights are on, turn the key, but nothing, no sound whatsoever. Then, for some reason the throttle cable has a high pitched hum. If I shake the throttle cable, it starts up again, although I know it has nothing to do with starting it. Starter was replaced with brand new Bosch, very pricey. There’s no pattern, it happens after a short trip, in the morning first thing, in warm weather, at night, sometimes only once in two weeks, sometimes twice in a row it doesn’t start. I have no commute, so this is used to make short trips all day, which is undue burden on the starter, but we replaced it. Can’t recreate situation so mechanic can’t really look at it unless it happens. Last mechanic had history of using old parts and charging for new ones, so ignition switch may be old. But it’s expensive to replace it. Everyone wants me to give up and buy a new car.

Check the wire which goes from the ignition switch to the starter solenoid. With a multimeter connected to the wire (ohms), just after the ignition switch and at the starter solenoid, shake the speedometer cable and watch the multimeter indication. The problem may be in the wire, bundle, or connector.