Several of the core guys were carryovers from the Parcells days, even with the latter two Super Bowl titles but there were plenty of key guys, even in the first title year, that were brought in by Belichick. Won't even mention the QB.
Bryan Cox
David Patten
Marc Edwards
Mike Vrabel
Richard Seymour
Then you had guys like Daniel Graham, Deion Branch, Rodney Harrison, Rosie Colvin, Corey Dillon, Ted Washington, Vince Wilfork, Stephen Neal, Dan Koppen, Ty Warren, Asante Samuel, Eugene Wilson, etc.... that were all brought in by Belichick one way or another.
If you wanna talk coordinators, then, yeah, BB won with Parcells guys in Crennel & Weis.