I had this happen once at a suburban hotel (a Marriott, not that it matters). It was one that annoyingly charged for parking, even though most hotels around it didn't and arriving by car was the primary way you'd get to the hotel.

Anyway, some giant ballroom event consumed all of the parking spaces. I street-parked a block away - legal parking, but a place you had to vacate or feed a meter by 8AM - and asked them to waive that day's parking fee. FDC ended up waiving *all* of my parking charges for the 4-day stay as a goodwill gesture.

Your situation sounded worse. I only lost 5 minutes since I could tell their lot was a circus and I knew the street option was there. I'd definitely want the parking charge for the day taken off, and probably a bit more than that.

I would guess (hope?) they won't put up a fight. Management had to be aware of the extreme parking situation if their valets were blocked in.