I know everyone say this, but if you're really that serious about exercising, talk to your doctor and see what he can recommend.
Aside from that, there's plenty that you can do that's low-intensity. Yoga and tai chi are very easy on the heart, especially if your breathing is focused. Muscular endurance exercises are usually fine as long as you're not lifting a lot of weight, and you're making sure you're breathing properly. You could try an easy bike ride or swim if walking's not your thing. Of course, listen to your body. You can push yourself but if you feel sick or lightheaded stop immediately.
