Is this the pin in the power connector inside the laptop thats broken?
I have never seen that connector broken but have had plenty of the plugs on the end of the psu fail on the type of psu that the nx6110 uses which is easilly fixed by fitting a new dc power plug. Unless the machine has a docking station connector on the base (i think only the nc models did) the only solution i can think of is to get the connector replaced. I have just looked at the board from one of these machines and it dosent look to much of a challenge theres easy access to the connections to solder the new one in. So it would suggest the repair shop you went to doesnt like repairing the boards or your board is damaged beyond repair. The hp manual that covers the disassembly of these machines is at
http://h20000.www2.hp.com/bc/docs/support/SupportManual/c00502970/c00502970.pdf
I have a a couple of these machines fail where they would freeze on post intermittantly both boards failled totally a couple of months later. so if you was experiencing that problem prior to the connector breaking i wouldnt recomend the expense of getting the connector replaced. I did a quick search on the web and found one place doing repairs for £100 but that sounds a bit steep for something as simple as a replacement connector.
Andrew
January 2009