If your time is valuable, and you do not wish to invest in this as a learning experience, then it will certainly be cheaper to buy a new kindle. For a touch, I recommend buying connectors for it instead of soldering to it, especially if you do not have tools or skill for surface mount soldering. Better to practice soldering first on discarded electronic devices.
There is an entire thread devoted to kindle touch serial port recovery.
If you are still interested, read here: