If some keys work then the electronics are probably ok.
Use a magnifier around the traces to the keys that dont work, in fact try to find a common track that goes to all the keys not working, this might be where the break is, sometimes they can be real hard to find if the break is under the green solder resist.
The only way to effectively repair a break is to scrape away the solder resist around the break and solder a piece of wire acorss, you can strip some copper wire out of some old cable, headphones, power leads etc, you can jury rig a solder iron from a large nail and a heat source, but you'll need some solder.