No one said that there was no probable cause to enter Gate's home and that Crowley needed a warrant. He was required under Massachusetts law to provide his identification card and he refused to do so on at least 3 occasions (possibly four times), as he admits in his report.
Keep in mind, Gates was not arrested for breaking and entering, resisting arrest or any like crime. Had Crowley suspected he was the law breaker when Gates asked for his ID, he would have just gone in and arrested him.
You really, really don't want to go the legal route, you will not win.
Edited to add: You may want to read this post before you continue down this route.
http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=389&topic_id=6150586&mesg_id=6153141