Attempting to run it isn't a good idea and you'd probably just injure yourself. But if you go for a slow and steady jog/walk strategy, you'll most likely be able to get round okay. Even if you've been couch-potatoing it up for a bit, you'll still have some residual fitness from your more active days, and if you have walked 55 miles, you should be okay to shuffle/jog/walk 13. A couple of years ago I had shoulder surgery a week before a half marathon I'd entered. I was told not to run but did it as a fast walker with a couple of jog/shuffles along the way, and finished in about 2 hours 50mins.
I wouldn't worry about a specific training plan, as four weeks isn't really long enough to work with, but make sure you get yourself a decent pair of trainers, preferably from a specialist running shop where they can check your gait and get you kitted out with suitable shoes, and then make sure you get them worn in a bit so you don't end up with bad blisters on the day. Just get out for a few jog/walks each week, aim to do a longish fast walk at least once a week, and don't plan to run. If you try to do too much too soon, there's a real chance of injuring yourself and not being able to do the event at all.
Then on the day, start right at the back of the crowd so you won't be tempted to try and keep up with the faster runners. Good luck! 