If you've only been running for three weeks I wouldn't be concerned that you're still very sore in between runs and during runs, whenever I start a new exercise that I've never really done before I've found that I'm often sore for up to a week before I can do it again and it can take a couple of months to really get to a regular routine, especially if adding it on top of other fitness activities I'm already doing. The other stuff you've been doing has certainly helped even if you feel like you should be further along. The C25K is a great program but I wouldn't be concerned if you have to scale it, most people can't follow along with a P90X or CrossFit program exactly as prescribed for the several weeks starting out either. You'll get there eventually.
The good news is that it seems the older I get the better my "muscle memory" is and the quicker I can get back into an activity that I haven't done for a while.
I'm not necessarily training for a specific run like a 5k or marathon, all I want to do is get myself back into playing condition for rugby. I tore my MCL snowboarding two years ago and have never been able to get back to where I once was...I can still snowboard and do various other athletic activities, but I know I have no where near enough stamina to run, and hit, and get up, and run some more for an entire match. The fact that I'm a big guy (6'3' - 220) combined with my competitive nature doesnt help at all...I need to control my self and start slow, otherwise I beat up my knees and ankles and dont want to run for another week or two. And by then, I've already lost anything that was gained by the first run.