A very likely fault is in the charger - a break in the wire as it enters the plug. This is constantly flexed and the result is that a conductor may have snapped.
Either check this with a voltmeter (or teh spare unit if that works) whilst flexing the cable to see if the voltage goes on or off, or borrow a known good charger and try that before you assume its the computer. You may be able to buy a cheap charger for less than the cost of the repair, and if it proves not to be the charger, at least you have a spare!