You don't need the gym nor equipment for a good full-body strength training program. Your body weight's enough! The good thing about being weak is you don't have to stay that way... that's what strength training is for!
You can use SP's workout generator to create a program for you, too. Definitely ask your doc!
Here's one place to start: www.nerdfitness.com/blog/2009/12/09/beginn
With pushups, it's okay to do modified, or even wall pushups if you can't do full ones. The important thing about working out is knowing what you're capable of, and modifying until you get stronger!