I had done several restores from iTunes even as you did, start from scratch and not load from a previous backup. Unfortunately the problem continued. One of the differences between a normal restore and a DFU restore is that it allows the firmware to be updated, which relates to the WiFi. DFU (device firmware upgrade), it basically puts the iPad in a state which the firmware may be updated as opposed to just the software.
Nice, I will let Ipad Forums know if they do a DFU Restore. That just might fix my problem