I definitely think the couch to 5K program could be helpful to you. Sometimes people on here think no chronic cardio = no running ever! No chronic cardio means don't run/bike/elliptical for hours a day. I run 2-3 miles at about a 10 minute mile pace (so not fast) several times a week, and I don't think it's doing me any harm. 20 minutes of jogging a day isn't going to be a problem. It once you are better able to run at a slower pace, you will be in a better position to increase the intensity aka sprint.
No disease that can be treated by diet should be treated with any other means.