I'm at a loss for ideas

im really at a loss here been to two mechanic and they dont see the problem, My car…for some reason starts only once. My brake peddle gets really stiff after I turn the car off like when I go to the store for an example, the car dash light come on but the engine wont start so I figured it must be the Starter right? But it could be the Break booster but I dont know how the Break Booster and the Starter work with each other. When I leave it alone for an hour the car starts, that’s the weird bit. I’m going to the mechanic again and see what he says. I could really use some opinion. the reason the mechanic dont see the problem because it doesn’t happen when I take it to them, I’m just going to show them a video this time.

It will help to know the brand,model,year and milage of your vehicule.

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The brake pedal getting stiff after the engine is turned off is normal. Without the engine running there’s no vacuum power assist. You might get one or two presses of the brake pedal before the remaining vacuum
is expended. As for your starting problem; how old is the battery?

No it’s not. The brake pedal would go still after two or three applications of the brake pedal after the engine is turned off. Going still immediately is an indication that there is a serious leak in the vacuum system of the brake booster. Could be the vacuum line, the check valve, or the booster itself.

That also explains the hard to start situation. When the vehicle is cold, the PCM sends extra fuel into the engine to get it started. When it is warm, it does not this extra fuel to start. The vacuum leak lets too much air into the engine for it to start without this extra fuel.

Edit: apologies to @FoDaddy. I reread his post again and I think he just didn’t mean exactly what the first sentence says, at least as I interpret it.