As mentioned before, for "solder-shy" folks (and the delicate pads DO lift off with too much heat for too long), you can get conductive paint suitable for this purpose at most auto parts stores (sold as "
window defogger repair kit").
I used a similar product to repair an external computer keyboard after spilled coffee disolved some of the conductive traces on flex cable inside the keyboard. Painting over the gaps in the traces fixed it. Interesting that the traces on that particular ribbon cable were coffee-soluble...
Such a product should work just fine for kindle serial pad connections, just as
knc1 mentioned (but no need to special order it when a local auto parts store carries a suitable product).