7 years ago, I had a dealer pair a USED ECU which I supplied them with to my 2000 A8. My original ECU had a persistent internal error measuring atmospheric pressure after the underhood electric box flooded.
The important piece is...if the old ECU isn't dead, just defective, then it is pretty easy. They need to read the secret 4 digit PIN from the original ECU, then install the new used ECU which you will supply them with.
They need to tell the used ECU to dump the VIN information it has from the donor car and pick up the VIN information for your car from the Instrument cluster/Immobilizer. The way they do this is first input the secret 4 digit PIN of the USED cluster to allow access to adaptation. They then change teh PIN of the USED ECM to the PIN of your original ECM. The Instrument Cluster/Immobilizer then sees that this donor ECM now has the same PIN as the original ECM, and sends over your vehicles VIN info to be copied onto the donor ECM. At this point your used donor ECM is now an exact clone of your original. Done.
It should take a decent tech about 1 hour.
You can buy a replacement used Engine Computer for a 2004 1.8t in Canada here:
Search "Computer Box Engine" from the dropdown menu and for the princely sum of $50 Canadian (what's that in real money btw)it can be yours from Mikes Auto Parts in Stoney Creek.
If the car was in your driveway and you were the handy sort, I'd also tell you to buy a Super VAG K+CAN from ecutools.com in China for $80 and pull all the secret PIN numbers yourself. http://www.ecutool.com/Super-VAG-KCAN_1025.html
This assumes of course you already have VAG COM from Ross Tech - or some kind soul nearby will help you. I can check both boxes and have paired ECU's, Clusters and Immobilizer transponder Keys with no trouble at all.
$2800?? That's freaking insane. Theya are charging you for a NEW from AUDI ECU. You don't need a NEW one. A USED one will work just fine.
Here is a video from Ross Tech showing the pairing process. ECM swap starts halfway through the video: