@birdbrain, most likely you can rebuild the traces by using small copper wires. Do not use any epoxy or circuit writer pens. those are very messy and most of the time will not work properly and increase the risk of short circuits. Post some images of your attempts so we can see what you see.
That image looks familiar:-) Definitely no to the epoxy. There is no substitute for soldering. As for the tools, this is not a good area for hot air station and solder balls. You will need a soldering station and some source of magnification to work on this. To solder the connector and/or the components you will have to clean the pads and use plenty of flux. The reason why your solder may not stick could be a heat as well as a flux issue. This is not an easy task and I would suggest that you have someone with boardlevel experience do this repair. Check on here and see if there is anyone close to your location.