Check out the Boston Craigslist for Pats tickets. There's always a ton on there. Find a posting from an actual person selling theirs as opposed to postings that just link you to their website. Granted, you won't have the protection of using one of the fee-based sites, so it that bothers you, you'll have to look elsewhere.
As for the train to the game, it's kinda cool, albeit on the long side for the relatively short distance. It takes just over an hour from South Station and you'll be nearby within a few miles within a half hour. Then the train actually changes direction to go off the main tracks onto an old freight spur and the train literally doesn't go faster then 5-6mph the rest of the way haha.
It was $10 roundtrip last year, no one way tickets which I doubt would be an issue in your case. I've taken it in the past to games when I was late getting out of town for the day and then just drove home with my buddies.