The fact the LED is not extinguishing shows the immobilise to be armed hence why it will not start.

If someone has messed with the transponder the red or blue "Chip" in the key this will be the most likely reason.

There are different versions of the PATS system the older versions which yours maybe has a red key, this is known as the master and you need this in order to program other keys.

I suspect it is nothing more than the key that is wrong.

Martin