The biggest problem with dieting without exercise is that the pounds you lose won't be the best kind. If you lose muscle, your metabolism will become slower and you'll have a harder time maintaining the lower weight. If you engage in at least some moderate exercise, you'll reduce the amount of muscle you lose in favor of losing fat, keeping your metabolism burning and give you a nicer body-shape.

Of course, as in go, and everything else in life, the key is balance. Too much of one thing or the other is as bad as too little. You'll actually be fairly miserable if you stick to a "perfect" diet. Even the very serious athletes have "cheat" days. Likewise, too much exercise, or too much of a particular kind of exercise will interfere with your life, make you give up out of frustration, or even tear your body down if you get to the point of over-training.

I think it's easy to underestimate the value of hitting the weights. Add a few pounds of muscle, and you burn more calories all the time. Calisthenics like push-ups pretty quickly become too easy and it's hard to add additional weight. Once you get to even like 15-20 reps, there's almost no benefit to doing more (if you want to work on endurance, running or whatever is better). One major exception are pull-ups. They're harder to start with and you can add weight with a weight belt or holding a dumbbell between your feet.

I respect your interest in keeping things simple and not wanting to add equipment, but at least consider adding some sort of weight training down the road once you get broken in and your back is better. It doesn't have to be complicated. Hitting the major compound lifts a couple times a week will make a world of difference.

Of course, the exercise routine is only part of the battle. You will have lackluster progress without proper nutrition. Likewise, any diet is virtually useless without proper exercise.

Tell that to these guy.
http://www.youtube.com/watch?v=T9QeitaeBrY
http://www.youtube.com/watch?v=TLCWMVkM ... re=related
This is what I'd like to emulate. Since calisthenics involving only body, at the higher levels involves mostly core strength, it makes you a more well rounded athlete. Plus I just really want to keep it simple. A combination of both weight training and aerobic exercise won't give me the core strength that I'm looking for.

@CarlJung
Just in case the purpose is to attract females of the opposite sex, (or men for that matter), you haven't forgotten the 23 July have you?

Well, you would have to think 5 years back. But maybe I am only confused, wouldn't be the first time.

That's some impressive upper body strength and endurance, but nothing for the legs. I guess that's where running comes in. Btw, why do you want core strength? Is it severely lacking and affecting other things? I see it mainly as a vehicle that allows me to do other things better and without risking injury.