Unless you are putting this pressure on the actual wires going into the molded plastic of the power cord's plug, I agree with JMPC. This is probably the notebook's jack the power cord plugs into that has broken, or broken loose. They are not very robust. Unless you are REALLY comfortable disassembling and reassembling complex electronics (with no left over parts
), I would take it to a shop.
As noted, sometimes a wire breaks off and needs a steady, experienced hand to solder back on. Other times, the contacts lose spring tension resulting in poor or no contact. These can sometimes be bent back but that is typically a temporary solution because the tempered metal becomes weak after being bent a couple times and can easily be bent out of shape/position again.
Sometimes the jack breaks out of it's plastic housing holding it in place. This can usually be fixed with a careful application of epoxy putty. In a couple case, the jack needed to be popped back into place.
If the jack needs replacing, the part is not very expensive. And once the notebook is disassembled and the jack is exposed, it typically is not hard to replace or epoxy back in place.
This is a common repair job so any experienced technician can easily do this with no more than 1 hour of labor, plus the part. Since they've done it a bunch of times, best to let them do it. They know how to hold their tongue just right to open the case.
And since there is no real troubleshooting involved here (troubleshooting is typically the hardest and most time consuming part of electronics repair) most shops should be able to give an estimate or actual cost before the job begins. So call around. And make sure they clean out all the heat-trapping dust while they have it open (as any good shop will do automatically anyway). In any case, as notebook repairs go, this should not be a budget buster.