Toshiba Satellite A135-S4427 bad power socket?

My wife has a Toshiba Satellite A135-S4427 and at times when plugged in the "plugged in" light isn't lit and the laptop runs on battery. right now we have it on a wood table and not moving it and it stays running as plugged in. How can I determine if the problem is the power cord or the jack in the computer? if it is the Jack, can it be repaired?

Yep, that sounds like a bad socket. You could test by taking a similar cord from another laptop (a friends maybe?) being really sure to match up the voltages, and plugging it in.

The jack can be repaired, but I haven't personally done it. You have to open up the laptop, find the jack (shouldn't be hard) and resolder a solid connection.