Most burn, least impact

We're talking least impact physically and financially.... My shoulder has been tweaked for a couple of months now (chiro said it was rotater cuff last time I was in...) and my knees have been hurting with how much I've been biking (to work and back daily the last week). I'm on a tight budget, so a gym is out of the picture. Beyond my bike and 2 legs, I have 5 lb weights, wii just dance and basic sports games, and pilates video (which I can't do much of....last time I tried, I felt more like a flailing, dieing walrus). Oh yeah, and a punching bag..... Any thoughts? I know I can just eat at a calorie deficit, but I want to be in a healthy habit of exercising....without injuring myself further. Maybe a youtube video you workout to? Any recommendations? And I really want to strengthen my core...