| Of course you can set your sights on some sort of running competition. Anyone can but it requires some patience! My husband started like you. He actually USED to run, and I caught the running bug from him when we were dating (13 years ago!) but he has since gotten wayyy out of running shape and until very recently couldn't do more than 3 consecutive running minutes without walking.
What we did was find a plan on runnersworld.com (higly recommend browsing through that site) that is actually called "the couch potato to 5K plan" haha. He is now up to running 5-6 minutes at a time and walking 30sec-60sec between and repeating 8-10 times. He runs 5 days a week with 2 rest or cross train days. His goal by the end of this month is to be running a mile, walking 30 sec, run another mile, walk 30 sec. By the end of next month he'd like to be running 3 miles continuously and enter a 5K. His ultimate goal by may is a half marathon at his goal weight. Baby steps for everyone-thats how you reach those big goals!  | 
