I drive a TDI. Have been having problems getting it to start when it's cold out, especially when it's in the low 30's in the morning. It can take me up to 40 times turning the key to get it to start. When it's not as cold, can take me up to 2 to 6 tries. The radio comes on, and the vent, when I turn the key, but the car does not turn over (no crank). I have turned the key so that the radio is on for a minute, and then try to start again, per someone's suggestion, but have not had luck with that. I had the battery replaced, mechanic said the glow plug is fine. He thought it was the ignition switch, but when I brought it in, he said the battery cable main Terminal 30 wire was loose, tightened, load tested charging system OK, and not other electrical issues were detected, but the next morning I had the same problem again. When I leave the car in the garage, I have no problem starting it. After I have started the car in the morning when it's cold, I have no problem getting it to start for the rest of the day. I bring it in for regular oil changes, just had the R& R intake manifold cleaned out with new interior filters because of sluggish performance.
If it does not crank, do not waste your time looking at the glow plugs or intake manifold.
On your vehicle a very common problem is that the ignition switch overheats and melts the wires/connector underneath the steering wheel.
Another common issue is that the starter solenoid wire sometimes breaks or has a loose contact. When the vehicle does not crank, I would remove the solenoid signal connector and test to see if you have proper voltage there.