2004 audi a4 1.8t quattro making screeching noise from engine upon startup. then noise goes away after about a minute. Then after driving awhile there is a burning smell.

You have a pulley wheel that is starting to seize up because the bearings are dry. You will have to figure out which one. Could be alternator or A/C. Where ever you see your belt go on a pulley, it could be any one of them.

Hmmm.......Ok! Thanks! Would you have any ideas as to what repair costs I should expect? I usually go to my independent German car repair shop.

Depends on what is seizing up. If something easy to reach like the alternator, it should not run more than an hour labor. If buried deep, like an A/C unit, it will cost you more. It all depends on what and where.....

Thank you so much! I'll update as to which it turned out to be.

That would be nice. Most people just drop the issue once they get the car fixed. They rarely ever post back to let you know what the issue was. Kind of defeats the purpose of this site. The guys that offer up solutions never get an update, so we never get to learn anything new or keep the solutions in our memories. I suggested putting in a box for the people asking the questions to enter the solution, but the web masters never went for it......

So, Here's what my independent German repair shop found........ the noise is coming from a bearing going bad in the "secondary air pump". Was advised to do nothing for now. The burning smell apparently came from packing grease slung from cracked cv boot on front right wheel. Have had problems with that wheel in past 6 months. (broken clamp repaired twice. boot repacked). cv boot finally bit the dust. As to your advice as to what the trouble was with my vehicle, they said that that was a good guess/ viable possibility without having the opportunity to look under the hood. I appreciate your input and expertise!