This happened to my housemate a couple of years ago, except she discovered that the birds were nesting there because mites from the nest started to infest all of the stuff near the window in question (the nest was there for a while - I don't recall what time of year the mites arrived so I can't estimate and she doesn't live here anymore). So, just a vote for "remove the AC and clean out the nest." The birds should be OK, if mad.