The car won"t crank, 1992 Volkswagon Passat

sounds like you need to get the battery checked as well as wire connections between battery and starter. 12.52 is marginal as when you crank the starter the voltage probably goes below 10.0 volts and when you jump it the voltage is at the proper level to allow cranking.

Probably blew fusible link. Check your positive battery cable for a break

First let's define some terminology. The job of the starter motor is to "crank" the engine, if it does this, weather the engine runs is going to depend on the fuel system and the ignition system and good compression. Try this: with one hand, hold the key it the "crank" position, with your other hand, move the gear shift (slowly)from park to reverse to neutral to drive. Make sure you foot is on the brake as it may start in gear. If it starts while doing this, you have a bad neutral safety switch.
Also, It wont stay running when you crank it by jumping the starter if the ignition switch is off. Try doing it again with the key on. If it starts with the key on, and you jumping it at the starter, you probably have a bad, or out of adjustment, ignition switch. If it does not start, with the key on and cranking by jumping the starter, then you probably have a fuel or ignition problem.
Try the above and get back to me. I can walk you through how to check for fuel and spark if it still wont run.

Is the security light on or flashing ?
The yellow wire goes from the key switch to the neutral safety switch, then to the starter. So bypassing the neutral safety would make the starter crank the engine, but would have nothing to do with the rest of the engine.

If you are saying it won't crank sometimes, you could try it in neutral instead of park. The neutral safety switch may be going bad.
Or you could check for voltage on the small wire going to the starter solenoid, it comes from that switch.

Are you saying the engine cranks but won't start, or the engine won't crank ?
If the engine does not crank, you would check for voltage at the starter, the neutral safety switch, and the key switch as well as the ground connections.

The ignition start circuit is the path from the ignition key in cranking mode to the solenoid on the starter. The path travels through a starter relay and a neutral safety switch before it reaches the starter.
This must be the circuit not working on your car.Make sure battery and starter connections are tight.Check for power at the starter solenoid terminal with a testlight when someone turns key to crank. If you have power there, they sold you a defective starter. If you have no power there then it could be the relay or the neutral safety switch.

COULD BE FAULTY TRANSMISSION RANGE SWITCH OR NEUTRAL SAFETY SWITCH.

if this was your problem before a new battery was installed, check the fusable link wire at the solenoid for it may have a internal break under the insulation
All cars have this inline link for fire protection to the engine

MAKE SURE YOUR BATTERY IS FULLY CHARGED.IT SHOULD BE 12.5 VOLTS.IF NOT HAVE IT CHECKED OUT AT AUTO ZONE OR ADVANCE AUTO.IF BATTERY VOLTS IS GOOD.MAKE SURE BATTERY CABLES IS CLEAN NOT CORRODED AND NOT LOOSE.IF BATTERY CABLES GOOD.HAVE STARTER TESTED.WARNING TAKE CAR TO VOLKSWAGON DEALERSHIP.BECAUSE IF YOU HAVE TO REMOVE THE BATTERY OR STARTER.BY DISCONNECTING BATTERY CABLES. YOUR PCM WILL LOSE IT MEMORY.THE CAR WONT CRANK IT HAVE TO BE RESET WITH A SPECIAL SCANNER.