May be worthwhile to pay someone who can open it up for you and do the
repair.

Another thought ... did you check to see if it was the external supply plug
that had broken its cable strands (not the plug receptacle on the laptop)?
Less likely, but if that is the problem, then the fix is much easier. Just
get a voltmeter and see if the power (18V I imagine) is consistently there.
You may have to rig up a way to keep the leads attached to the plug.