I went to move the car into the garage to replace the exhaust system. After starting and releasing the e-brake, I found a rock-hard brake pedal, with NO response at all to the brakes. I don't know jack about ABS systems. The fluid is up. There were absolutely no warning signs. Anyone else had this problem? Thanks in advance.

brake master cylinder probably needs to be inspected by your audi mechanic.

Seems like the master cylinder locked up, or the brake assist pump, or booster isn't working right. Am shooting in the dark though.

Rock hard brake pedal = no servo assistance its nothing to do with your ABS system .You could have something as simple as a collapsed servo feed pipe.

'hockey" is exactly correct. You have a bad brake booster (power brake unit), either due to a defective unit or a vacuum hose leaking or popped off.

Your brakes didn't "fail"...if you pressed hard enough they would stop the car.

Shop around for repairs...old Audis are not cheap to fix and I'm sure even a rebuilt booster unit is, sad to say, not going to be cheap. Maybe you'll get lucky and they'll find a disconnected or broken vacuum hose.