Vw beetle does not start. seems like its some kind of anti theft protection. the car/key icon lights up, it turns over for a second , then off. this is the first time this has happened, but we bought it used last year, with no owners manual, and just one key.

Because you have changed the Module twice, (to the replacement one then back again), You will have made the ECU, (the car's brain), think it is actually being stolen. You'll need a Good Auto Electrician to look at you vehicle to sort this out.
Anti-theft units are coded specifically to the vehicle it is originally fitted to and only that vehicle so it can communicate with the ECU and the Key fob. That means they are not normally a part you can just swap. The only way to swap them is to pay the Silly prices and get a Dealership to re-programme the ECU and the Anti theft module to match your vehicle.

Anti-theft system can keep vehicle from starting , Alarm is for vehicle content theft , open door without key alarm sounds (horns) ! PATS - passive anti theft system PATS enables and disables the engine from starting ,it will not cause the engine to die ! You have some other kind of problem ! If the vehicle engine doesn't turn over an red light on top of dash flashes fast ,then you have anti-theft system problem !
PATS differs from the perimeter anti-theft system in that PATS enables and disables the engine from starting. If equipped, the perimeter anti-theft system protects the perimeter of the vehicle (doors, hood and trunk) and sounds an alarm.

NOT ANTI-THEFT YOUR THROTTLE BODY MEMORY HAS BEEN LOST YOU WILL HAVE TO BRING IT TO VW OR SOMEBODY THAT HAS A SCANNER THAT WILL RESET THROTTLE BODY CHANNEL 98

This sounds like the anti theft system is active, you jump start it but it dies out after a few seconds , if this is correct then try another key. the other thing can be a weak battery make sure the battery is fully charged and good,

TRY REPROGRAM KEY .PUT KEY IN IGNITION SWITCH TURN IGNITION SWITCH ON POSITION 20 SECONDS DONT START ENGINE WAIT 20 SECONDS TURN OFF SWITCH THEN TURN SWITCH BACK ON 20 SECONDS WATCH THE THEFT SECURITY LIGHT BLINKING.WHEN THEFT STOP BLINKING VECHICLE WILL CRANK.IF LIGHT STILL BLINKING.TRY FEW MORE TIMES KEY IN SWITCH ON POSITION FOR 20 SECONDS.MAKE SURE YOU HAVE THE CORRECT CAR KEYS IN SWITCH IF NOT WRONG SET OF CAR KEYS WILL SET OFF THEFT SECURITY SYSTEM.IF KEY RESETTING TRICK DONT WORK.CHECK BATTERY POWER MAKE SURE YOUR BATTERY HAS 12.5 VOLTS AND CHECK SECURITY THEFT FUSE.IF ALL LOOKS GOOD YOUR SECURITY HAS TO BE CHECKED OUT AT THE DEALERSHIP.

Hopefully you are using the same ignition key you had before to start the car. This flip module mhas a chip that tells the system you have the proper key. If for some unknown reason the system lost this program it is probably a dealer only problem. The chip is inside the fob right near the key itself.

It has to due with the anti theft system. Try replacing the battery, when my battery went bad the ecg light came on and the car wouldn't allow me to drive. That or your key may need reprogrammed by the dealer.

take the positive side of the battery off for about 3 seconds and then put it back on to see if this will reset the security code

you need to check the drivers door lock unit. this is a more common problem where the switch fails and the anti-theft system doesn't get disarmed by the door unlocking