The Patriots bandwagon got rolling in 1993 when they hired Parcells and drafted Bledsoe. It accelerated with earnest when Kraft bought the team. It wasn't 2001 or 2004. It was 1993.
The late 80's/early 90's Patriots were the Cleveland Browns of their day. It was an investment and the owners (Victor Kiam, and then James Orthwein) looked to get the biggest return for the least amount of money they could, and the product reflected that.
The fact that they played in a stadium unfit for a Texas high school didn't help, nor did the Lisa Olson scandal, but the Patriots were often blacked-out in the local demographic back then. The blessing in disguise was that Victor Kiam could not buy the stadium with the team. Kraft out bid him and got the lease rights with the Patriots. So when Orthwein (a Busch, of Anheuser-Busch notoriety) was exploring moving the franchise to St. Louis, Kraft wouldn't let them out of the lease.
"Following the NFL's approval of the sale, the Patriots sold out their entire 1994 season..."