Want to drop some knowledge on you in case someone's googling. (Since there seems to be a lack of answers.)
Looks like a very common problem on the Inspiron 1520 - plug in charger, light goes out, seems completely dead. (Shorted.)
The cause of that, which I've seen and fixed on two occasions now, are the tantalum power caps near the processor: PC41, PC42 and the adjacent two pairs. They're 1uF, 10V, 0603 package.
I can't yet tell you the reason why they pop, but they do.
The schematic can be found on this here forum and the caps can be found just north of the CPU power coils, between large transistors.
Hope this will help somebody.
-edit-
Note that if your replacements are a bit off, lets say by 0.5uF, it'll still work, but you'll get nasty coil whine dependant on the load. If you can, measure your parts beforehand.
Looks like a very common problem on the Inspiron 1520 - plug in charger, light goes out, seems completely dead. (Shorted.)
The cause of that, which I've seen and fixed on two occasions now, are the tantalum power caps near the processor: PC41, PC42 and the adjacent two pairs. They're 1uF, 10V, 0603 package.
I can't yet tell you the reason why they pop, but they do.
The schematic can be found on this here forum and the caps can be found just north of the CPU power coils, between large transistors.
Hope this will help somebody.

-edit-
Note that if your replacements are a bit off, lets say by 0.5uF, it'll still work, but you'll get nasty coil whine dependant on the load. If you can, measure your parts beforehand.