In the early 70's they didn't have a home, going from Fenway, to Nickerson Field to other locals, had an underfinanced ownership and a product on the field that was substandard to say the least... They were definitely among the lower end of the bell curve for franchises and it is tough to think of too many lesser ones of the time... If as wrote, you started following the team in 1976, you don't go back far enough to remember the pre-Foxboro stadium days..
The first game they played there ( August 15, 1971) got preempted on TV locally when President Nixon chose that moment to announce wage and price controls and when everyone flushed the toilets at the first break in the new stadium, they overflowed..... a fitting visual for the franchise then.....