well... by the process of elimination... if you have a known-good power supply that charges batteries in other laptops, and you have known-good batteries that charge in other laptops... sounds like...

an update:

replacing the (external 19v) power supply may very well work.

i have a dell inspiron 8600 with the same problem.

dell tech support advises that the power plug (hole) in the back of the laptop is (of course) soldered to the motherboard and that it works...

i've had mismatched cpu's on a motherboard. it likewise would not boot.
both intel cpu's had the same numbers stamped on them, were the same speed, l2 & l1 memory, etc.

i had to send both back...