What the hell is wrong with me?

Why can't I run? Why can't I, after more than two months of regular running, run without leg and/or lower back pain? Two months is what it generally takes people to get fit enough to run 5km without stopping. I have to push myself to the limit to run 5km in 800m intervals in 30 minutes.
You would have thought that I would have settled in to a nice pace and stride by now, but no. It's an eternal fucking struggle against the pain and the awkwardness of running.

I can imagine that most people, after running for a couple of weeks, settle in to something akin to walking at a higher pace. You don't really have to think about the technique, you just do it. Me, on the other hand, I have to think about every fucking step. It doesn't matter what I do, I can't seem to get a good thing going.

As if that wasn't enough, the pain just keeps coming back. I recently took a week off from running to heal my legs. I started back up on Monday, and it took about 500m before the pain was back again. Same locations, shins and calves. Not to mention the lower back, but that doesn't set in until about 750m.

The worst things is that I know what causes all these problems, and I've done everything in my power to alleviate the problem, but nothing works. I've tried long stride, short strides, hig knees, straight legs, landing on my heel, landing on my full foot, landing on my toes, landing with my leg straight, with my leg bend. Nothing I do takes the pain away, NOTHING!

What the hell am I doing wrong? I've read just about everything I can get my hands on about my problem, and tried everything therein to fix it, but it has all been for nothing. I'm going to give it a couple of more months. If I can't run 5km without stopping and without pain by the time fall rolls around, I'm going to consider running a dead sport to me.

The only thing I can think of that could be causing this would be my crappy bio-mechanical conditions. My foot arches are different from each other, my feet are of different size, my legs are of different lengths, and I have suffered from a lot of back pain in the past, due in part to this. Getting a proper chair fixed almost all my back problems instantly, but apparently that doesn't extend to running.

I hate the situation I'm in, and I don't want to quit, but I'm affraid that I might have to. If I do quit I won't do it without having given it a proper try. By the time september rolls around I will have been running for five months. If my problems haven't been solved by then, I'm affraid I'm going to have to admit defeat.

Fragility

Why the hell am I so fragile? Why isn't 24 hours enough to recuperate from 30 minutes of running? I've been running 2-4 times each week now for little over two months, I have proper shoes fitted by a specialist, I run on a soft surface (track), and I still end up with sore muscles after each run. I need 1-2 days of recovery in between sessions to not break down completely, and it's pissing me off!
You would have thought that my body would have adjusted by now, but noooooooooo. I'm doing everything by the book, yet I still break my body each time I lace up. I's incredibly frustrating, especially since there doesn't seem to be anything I can do to get better. While my stamina has increased (5km in 30 minutes, with some walking inter-spaced), I can't seem to get fit enough for mu muscles to handle this simple thing of a run a day. I'm not asking much. I'm not asking for hours each day, or a triathlon each weekend, just grant me 30 leisurely minutes of running each day, is that too much to ask?
Here I am with an ice pack on my shins, having to cut my run short after 20 hellish minutes before admitting defeat in the face of having to spend 1-2 weeks not running at all should I continue and completely trash my legs. Today it even got to the point where my thighs started hurting. My thighs! My thighs never hurt, normally. It's always my calves (less so lately, however), and my shins (always a fucking pain). I stretch and I do toe-raises as my desk daily, but that doesn't seem to help the fact that my shins never get with the program. I guess I could spend 2-3 weeks completely off running and physical exercise to let them heal, but then I'm back to square one again. I will have lost my stamina, my remaining muscles will have weakened, and I have to start building them up again, which inevitably will kill my shins.
It's a vicious cycle, and I don't know how to break it.
Help me Obi-wan Kenobi, you're my only hope!

Shin Splits

I recently started running. I've been running for about four weeks now. I even got new shoes.
There is, however, a very annoying problem. I've got anterior shin splints, and they don't seem to want to go away.
I've tried different running stiles, different strides, different landings, different knee motions, different breathing patterns, different running material, nothing helps.
Here some people will say "dude, you have to rest and they will go away..."
But dude, I did! I stayed off my legs for a week (ok, 5 days, I cheated a bit), but they still came back in full force. As soon as I took the first step at any speed over walking, they started creeping back until they were like little goblins banging on my tibea with sharp rocks. As soon as I stop, though, they go away. The pain is not pervasive in any way, but it really keeps me from running.
I also don't want to wait for too long (without running, to recuperate), for fear that I'll forget what motivated me to run in the first place, and the flame will die. I do want to run. I used to run when I was younger, and it's a great way to stay in shape. The problem is that it hurts like a motherfucker, and I have no idea how to stop it from doing so, short of not running.
Any suggestions are welcome.