I brined one turkey years ago (before I had the healthy guidance of this great place) and my results sound alot like what you got. Back then I cooked my turkey in the oven but it came out rubbery and tasteless.
I think my problem was same as yours, too long in the brine. Since that awful experience I have perfected the cajun injected smoked turkey. It is a favorite at my house.
I'm trying brine again this year but will do a practice run before Thanksgiving and will follow the Turky 101 pdf that's been circulating the forum for the past month. Do a search for it, best guide I've seen.
Bowl Bound and B-B-Q-in! Sic Em Bears!