The jack is loose correct?
Is the other HP you have an 8440p as well? If so, charge a battery in the other one and swap it into the broken one. If the laptop powers on with the good battery (no ac), then I would take it apart to look at the solder points on the power jack. If not, then you likely have a motherboard issue. I would rule that out before buying a jack/opening it up (because it would be free and easy).
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Silverstone SG07
Asrock Z77M ITX w/3770k
Asus HD7870 2GB
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Corsair 240gb GS
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