Hi, I had the same problem for about 3 years and it seems to be a common problem with other users. I also tried new chargers and batteries with no luck. I finally tried replacing the power supply circuit board and now it's charging (original battery and power supply). I ordered one off of e-bay for < $5 with free shipping:
It wasn't too bad to replace. You just have to get the keyboard out of the way (here is a video tutorial http://www.youtube.com/watch?v=OPvSLJL6fJg). You may have to remove some other mother board cables to lift off the molding far enough. Then take out 2 screws connecting the motherboard to the power board, and then one more screw holding the power board down to the base of the laptop. Plug in the new one (make sure it the connector mates to the mother board), and it should work.
Try to avoid breaking anything 🙂
I should say that other forums have commented that the ebay boards are cheap quality and sometimes quit working. I'll let you know if mine dies anytime soon.
They suggested buying from here: njrefurbpc.com/.../dell-inspiron-1525-1526-dc-jack-charger-board-48-4w006-011-48-4w006-021.html