Hi,
The '''DC''' socket that accepts your AC to DC adapter cord plug is part of a module known as the Power/ Battery Pass Through Board.
Here is a link to the service manual for your model netbook. Scroll to p.66-67 to see how to remove the board.
The board is connected to the motherboard via a cable connection.
http://tim.id.au/laptops/hp/hp%20mini%201101%20mini%20110%20compaq%20mini%20110.pdf
The part number for the board is 537615-001. If you "Google' just this number you will get suppliers for the board. Here is just one so you can get an idea of what it looks like and what it may cost. There are others which may suit you better.
http://www.ebay.com/itm/NEW-For-HP-Mini-110-537615-001-DC-Power-Jack-Board-Connector-Retail-/191212784373