hi Raz,
I realise that it is a little late, but before you start using a soldering iron on any battery powered portable equipment, remove the battery first.
The failure of the DC input socket on laptops is a common problem due to bad design.
The socket is not screwed down, it is held in place by the thin plastic surround, so eventually as the plug is removed and reinserted the socket becomes loose.
The wires to the back of the socket are much too short and one will break off due to the socket moving from side to side.
I have have to repair 3 laptops this year with this problem.
Laptops are not designed to be repaired by inexperienced consumers. There is any number of reasons for the death, almost all of which point to complete destruction. Without more information from you it's impossible to tell you what could be the problem. We need pictures of EVERYTHING, really. Your power jack, your motherboard, other portions of the laptop, any labels you have on the computer, etc.