1st you need to know the remote lock & the immo chip for starting are 2 seperate items not linked but both work from the fob, thats why locking works as its seperately working, the icon means the immo chip isnt working intermittantly, you wont need to recode if it works still, have you tried with the other key see if makes any difference as could be barrel which makes the chip allow starting
The key has a chip in the top of which is only operated when near the barrel as it then uses an inductive field to read the chip which then allows the car to start, the remote is just a small pcb that you can code yourself with vagcom to lock/unlock the car, the immo chip however is a dealer job now or a professional car key person & even thats hard these days with the new systems in place by audi, the dealers dont do anything anymore, all done down the pipe from germany over net, dealers dont see skc codes, anything anymore.
New keys have gone down in price I believe, try audi 1st mate as I wouldnt trust external key guy as they could easily code a spare key for your car whilst doing yours.