Hi all, I want to thank all of you for responding to Shirley (my fiancee) so quickly.
Namely, I am not very car-savvy myself. One thing I am fairly sure I can distinguish is the "belt screeching" noise. I don't believe this is it. This sounds a bit more like scraping noise, whereas the belt noise goes a bit more towards a whistle/screech. Again, I'm ignorant when it comes to these things, so I may again be wrong.
Once the key is turned, the car starts fine, but toward the end of the initial starting "cycle", this noise come on as a loud noise that overpowers the engine noise and then it immediately dies down (does not linger like belt noise sometimes may) and the car starts and drives just fine after that. One thing to note is that this noise is sporadic, it seems to appear more often when the car is hot (we started the car from being cold and heard nothing).
In summary, this is what was done to the car, along with the symptoms in a matter of a week:
1) Oil and headlight change (Midas); car would not start in the Midas parking lot. Got their diagnosis for new starter.
2) New starter (Midas); car would not start in the Midas parking lot. Got their diagnosis that battery somehow got drained. Got a jump. Car starting making the screeching/scraping noise. Drove around for a bit, died again. Got another jump, went to dealership.
3) New battery (Dealer); Car sat for a few days, then would not start again. Towed to dealer, needed immobilizer reset.
4) One key reset, immobilizer reset (Dealer). Same problem with immobilizer.
5) All keys reset, immobilizer reset (Dealer). Car remains with screeching noise.
One thing we are debating is whether to take this car back to Midas (BBB requires that you try and address the issue with the business of your complaint, first and foremost) but since we have had now so many problems, we no longer have faith in their service and towing the car around after their meddling is not cheap. We are contemplating having the dealer just fix whatever has to be fixed and then pick the legal battle with Midas.
Again, thanks so much for all the responses so far, and in advance for any new input.