You need to have TWO working PATS keys in order to program another key.

Without that it has to go to the dealer with the programming tool or
locksmith that has the programming tool.

Whenever removing the battery on vehicles with this feature, there is a
specific place that 12V has to be jumpered into the vehicle to hold the
memory to prevent this problem. I would suggest that you never let the
battery run completely dead and replace it before it fails.

Wonderful feature isn't it. Say you leave your headlights on and the
battery is a few years old and drops below memory holding voltage.
Then you cannot simply jump start the car but have to either pay a
locksmith to come out or pay for the tow to the dealer, just for a dead
battery that in years past could have been jump started. In most
modern vehicles if the battery is really completely dead it is
recommended that you not jump start it as the alternator and charging
circuit has little extra capacity to supply the large current demands
of a completely dead battery.