Zero and Wifi 101- nothing happens on example sketches

I don't own a wifi shield, but I know that in some version of the bootloader, if the pin5 is tied low during boot, the Zero stay in the bootloader until you upload some code...
The schematic indicate that digital pin 5 of arduino is used as WINC RESET. The pin is pulled high on the shield, but there is a 10nF cap between D5 and ground on the shield, after a level shifter, and 100nF between IOREF and ground. With the 100k pullup it means a 10ms charging time before the level shifter and 1ms after.

Maybe those cap are not charged enough for the SAMD21 chip to see a HIGH level on pin 5 right after powering the board...

You should try to update the samd core with the 1.6.2 version. Then burn the bootloader using either Atmel ICE or EDBG.
Here is the link to the part of the code that is disabled in the last bootloader that may cause issue with your boards : github link to bootloader