The vacuum pump in the trunk runs the door locks.
You will only have power during the process that they are cycling i.e. when you turn the key in the drivers door lock and it turns on to lock the doors or unlock them.

The heat issue is most priobably that you knocked a hose loose or broke a rubber connector while putting the radio back in. There is a vacuum pod that is right behind the radio that is most likely your culprit.

You can check if this is where the leak is without pulling the radio and ashtray by checking the vacuum control valves on the passenger side of the console. You need to remove the kick panel under the dash and the carpet on the passenger side to access the valves. With a MityVac you can test each circuit by plugging in and pumping up the vacuum to see if they leak.

Either project is not too bad but takes some time and patience.

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'99 S420 - Mommies
'72 280SE 4.5 - looking to breathe life into it
'84 300SD Grey - Sold
'85 300SD Silver - Sold
'78 Ski Nautique