
Luckily, you can usually find new replacement keyboards on eBay realitively inexpensively. These traces are often on flexible plastic, it's very difficult to try and fix these. This often happens if a liquid was spilled inside and corrodes the trace. If you break a wire in the matrix, you'll knock out several keys. A broken trace on it will affect several keys. Now, the reason some of your keys is not working is you have a broken connection in the keyboard. On a desktop keyboard it's the same, except the controller is inside the keyboard, providing ps/2, usb or other interface to the comouter. The controller on the motherboard scans the matrix to see what key was pressed. Google keyboard matrix and also look at image results for a better understanding. The reason there are less connections than keys is that the key switches are arranged in a matrix. On a laptop keyboard the controller is usually on the motherboard - no active circuitry on the keyboard itself.
