Car died and now alarm will not turn off.

Not sure about the dying may be an oxygen sensor going out. The shaking may be your allignment needs fixing.

Old new beetle VW harness has contact resistance problems(vibration of wires) and needs to be recrimped the long wires(vibration can be stopped by silicone rubber anchoring). Cold weather make battery voltages low and needs recharged with handbrake on(headlamps off) 10 minutes warming engine up the whole winter.

try installing a new brake light switch ref. haynes repair manual for vw 98 - 2002.

using your remote key fob push the unlock button or use the key in the drivers door and turn it to unlock

Just leave the car battery charge up and then unhook the battery cabbles.........It should get enough charge in about 15 min to start without assiestance from jump start,...........Hope this helps.

get the ECU checked by an authorised service centre.

Take to dealer. Vehicle needs vag-com to be reprogrammed. Bring all keys with you to dealer.

My 2000 Beetle does same thing (although not all the time). Just found an internet post that suggests there is a problem in the door lock sensor. I assume you are using a regular key - not
the keyless entry - like I am. He also said that you can disable the alarm (also disables the
keyless entry - which doesn't bother me) by leaving the front door AND the rear trunk open and
starting the car up. Seems to work so far. I will get the door lock sensor replaced and turn the
alarm system back on (not sure how yet), and let you know if that stops the problem.

Brake lights it's a recall...

If you do not have a Check engine light on and you have an alarm system, try in disabling that first and then try starting it. Do not disable the alarm by pushing the button, you must completely disable it. Some systems will act this way mhen the key did not register