What could cause a VW Jetta 3 engine to not turn when cold almost as if the engine is seized

something is draining your battery, I would take it to an automotive electric mechanic .

Get a cheap multimeter and test for drain, sometimes it is the starter, check the battery at all off, and running, your parts I hope are warrantied have them both tested and checked, The starter and or coil can cause weird electrical issues and a bad ground could be causing everything to work harder. You need an honest mechanic who cares about solving the problems.

PROBLEM COULD BATTERY CABLES NEED CLEANING AND TIGHTEN OR THE STARTER OR STARTER SOLENOID FAULTY.

try to boost battery if starts alternator problem battery prob if it turns no start other problems no fire no gas etc you have to start from one step at a time to solve why so go slow and try one thing at time or go back to who replace engine did he tighten all i mean all cables such as starter wires ground wires etc battery and alternator

check starter relay @ look for burnt fusable links around starter area also check starter connections on starter.

Try spraying starter fluid in intake air-cleaner and see if that works

I would try replacing the battery some can become defective very quickly if car is left for a period of time.

If you live where it is cold, your battery may need to be replaced . They will discharge with the cold during the night. Try changing the battery or checking your curent one. Install a known good battery that you know is fully charged, start the car and then turn it off leaving it for the night. If it does not start in the morning then you know it is not the battery. More than likely the alternator or regulator.

mass airflow sensor, is a common problem when that happens, i have a buddy who had a 93 eagle summit that did the same thing as your jetta

If the engine wont turn over i doubt its fuel starvation. I would be looking at flat battery of faulty starter/ ign switch.