I've been to Best Buy and a local Smart Phone Medic
For what reason? Apple provides all hardware support for iPhones in the US. Hopefully neither attempted to open the iPhone. If they did, your warranty is now voided.
Clean the dock connector with a soft, dry brush.
If the problem continues, basic troubleshooting from the User's Guide is reset, restart, restore (first from backup then as new). Try each of these in order until the issue is resolved.