How can I repair my charger for my HP G72 laptop?

Bouzy, it is most likely the power connector. It has the highest failure rate due to constant bending and stresses from pulling and shoving. The "thick" cylindrical piece you circled is the ferrite choke to help prevent RF generated, from flowing back up the ground shield. I have not had a failure at that end. Yes, it can be repaired. Problem with that may be the availability of a new tip. You can check for some of the sizes on here, then check places like digikey.com or Mouser. com for replacements. It is not a tough job and can be relatively quickly accomplished. you will have to have soldering tools and soldering skills. Here is a site that will give you a pretty good idea. the only other way I know off, would be to open up the actually power supply, unsolder the whole cable from the circuit board, and resolder a new wire. Some of the adapters are very difficult to open, therefore that would be my least likely option. Hope this helps, good luck