2003 Audi A6 2.7T starting problems. Drove through

How long does it run? Sure you only changed the serpentine belt? The car would actual even run without the serpentine (or also called accessory belt) since the belt only drives fairly non essential components (AC compressor, alternator, fan, power steering pump. etc).

this gearbox is computer controlled,you will have to get it on the diagnostic machine to isolate the problem,we would all be guessing if we said its so and so.......

This is likely your electronic speed sensor. On my 2003 F150 it would rev quite high before finally shifting into 2nd. and my O.D light would blink also. The speed sensor is located under the vehicle about halfway back on the frame on the passenger side. The part costs about $70 and is a fairly easy repair.

change thermost and/or water pump

Audi A4 1.8 quattro 1997 automatic transmission does not change gears sometimes. It revs very high but the gear seems to be put in neutral

is the belt a fairly new one? if streched it can have the tensioner over extending causing it to leak or check oil preasure if to high will cause seals to leak, if all that is ok, then you may have a part problem

Could be thermostat this regulates the water flow around the engine to keep it cool sounds like it is sticking open when water gets hot!!

you may of dislodge a main fuse, check them for security and integrity

replace the thermostat , sounds like its not closing or does not have one , and make sure that your coolant is at least 50/50 (50% water,50%antifreeze ) if you got more water that antifreeze your system will freeze up in freezing weather

Are you getting spark to the engine? Also verify that the fuel pump is working.