Welcome to Flyertalk.

OK, as I understand it: You were on a 767-300 SFO-JFK and the seat would not reset, and didn't recline (JFK-FCO was likely on a similar aircraft, sold internationally as Business class - on a Business class ticket, though domestically they call it "First" on a two class aircraft). So, possibly a $4,000 Business ticket?

AA offered no refund (your other three segments you were seated in working seats, and on all four you received cabin service for the purchased class of service), but offered 20,000 AAdvantage miles (which AA values at $0.03 per mile).

For comparable compensation incidents, there are both archived and current compensation threads. We'll merge this into the current thread <link> soon.