HP and other makers must fix this the "absolute right way" by replacing the motherboard and incuring a high fee. Other repair shops like ikenfixit.com, notefix.com can fix it at about 1/2 that price.

While you may fault HP, take a look at the power connection on laptops at a place like a big Best Buy. You'll notice that none will take much abuse. Yes. abuse.

All must be treated with extreme care due to the nature of the design.