I suffer from back pain and I go for a two-pronged approach-
1. Watch your running technique. A bad technique will put too much pressure on your spine. This might help- nhs.uk/Livewell/c25k/Pages/... Maybe try going for a run a couple of times without the podcast just so you can concentrate on your technique.
2. Strengthening exercises specifically for your back. Lots of yoga poses can help, you don't have to do all the meditation stuff as well if you don't fancy it. I've been using this one- fitnessmagazine.com/workout...
Oh, and not too much time at your computer if you can help it! If you are stuck at your computer a lot for work then try swapping your chair for a swiss ball.
Have you had your current footwear examined? and a gait analysis done? If your shoes are collapsing to the inside (overpronating) your body will be misaligned and this will cause back problems.
A slightly different angle on it - try reading about Chi running. I keep going on about it, but the posture side of this makes so much sense. Much as has been said above, it's all down to running form, and how the different bits of your body work together (or don't).
For me, running is so different to how I've moved before, that I've decided I need to put a bit more into learning how to do it efficiently. So far, so good - the extra effort seems worth it. And I've been sitting on an exercise ball too, for some of the time when on the computer (although it's a bit low, so doesn't work as well as it might).
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