iPad will not sync with iTunes shows error 27 then 14 therafter

I have a iPad 3 4G with the 30 pin connection port that I purchased new from Best Buy a little over 4 years ago for almost $900. After my last update around 6 months ago iPad began to throw errors (27 &14) when doing a restore while connected to iTunes. After procrastinating for a while I called Apple Support and they did some troubleshooting. Apple tech made sure I had the current iTunes version. I tried multiple data cables that charged my kids' iPod without fail. After Apple Supports failure of solving the issue tech arranged an appt at the nearest Apple Store. Same issues occurred at the Apple Store with tech's MacBook Pro and his own data cables. Tech stated that the error 14 indicates a faulty charging/ data port. Apple Store said they could not fix and best option was to trade in my iPad and they would give me the same iPad just in new condition for $300. I figured for the advancement in the processor it probably wasn't the best decision. My iPad has never been wet and very seldom used compared to most. I mostly paid bills, emailed, & surfed the internet. Can this iPad be fixed? What is my best course of action? Thank you for reading & taking the time to answer. Happy Holidays!