First, swallow your pride, and go back home and apologize for running away. I know this step will be extremely hard, and you may feel like "screw my parents, I'll make it on my own!", but being homeless sucks and makes it even harder than it needs to be. Worst case scenario, if you can't join, at least you can go to college and do something with your life, rather than wandering the streets begging people for money or food.
Be humble about it too ("Mom, dad, I'm really sorry about running away, I thought I could make it on my own, but I realized how important you guys are and hope you'll give me another chance"), they may be more willing to take you back as well (as opposed to saying "well, you guys suck, but you're not as bad as the streets, so I'll give you suckers another shot.")
It sounds like your losing too much weight for it to be healthy. Although your parents didn't seem very supportive of your goal of joining, see if you can prove them wrong by working out everyday and studying, they may eventually reconsider their positions. After all, if you can't show them that you have the mentality and dedication to do what's needed, why would the military consider you over someone who IS dedicated and motivated?
The military is very physically demanding, so you should do it in a healthy way, by eating right and working out, not starving yourself, or worse, eating unhealthy foods.
How are academically? If you get good scores on the ASVAB (basically the military's "test" they administer to see how smart you are), then that opens a lot of doors for you (basically you can choose from a lot more different jobs than someone who scored really low and only qualifies for infantry). If you're not doing really well there, you may want to brush up your education first.
I think right now the military is more selective of who gets in, but again, if you're relatively smart, somewhat fit, and especially motivated, then you have a good shot of getting in, especially compared to someone who's fat and not working out, and thinks the military is just good for their resume, and lacks the brains to do the more technical jobs the military needs troops for.