Maybe you need to give running another go? Shin splints is probably just a result of poor form, or poor footwear, a good running shop will check your form and suggest some good shoes etc.. Since that's the one you didn't get back pain with, it seems worth a shot. If you find it boring maybe sign up to a 5k or 10k so you have a goal. Also, there's a moment by all accounts (not mine) with running that it just "clicks" and suddenly, the hard work fades away and you begin to enjoy it.
Otherwise you could join a beginner badminton/tennis club?