Did your doctor give you the all clear for exercise ? Ideally, it's always best to consult your doctor before starting or changing your exercise routine.
Now, if you have clearance, have you tried resistance bands ? You don't have to use weights to do do strength training. You could try resistance bands. Some come with handles. Some are just flat bands. There are also tubes that circles.
Even though you can't do a push up, you could try modified plank. That's the version of plank you do on your forearms instead of your wrists. a push up is nothing more than a moving plank. So, if you can only hold it for a few seconds. that's okay. that's a start. www.sparkpeople.com/resource/exercises.asp
Do you have access to a pool ? Swimming is a great cardiovascular exercise that isn't weight bearing. You could do water aerobics too. They even have aqua zumba. I also know of weight training/physical training devices that can be used in the pool to gain strength.
talk to your doctor and ask them if swimming or water aerobics are okay.