The MicroZed board in the evaluation kit is a 'standard' MicroZed and does have the USB-UART functionality.
The SiLabs driver normally installs automatically in Windows 7, as mentioned above, it can take a really long time the first time. You might want to uninstall the driver you installed and let the USB-UART driver install automatically if you can.
The other thing to check would be the USB port you have connected your MicroZed to. Make sure it can supply enough power for the MicroZed to operate (so no 'passive' or un-powered USB hubs). If you could try a different USB port, or even better a different Host PC, that could rule out any issues with your MicroZed board or cable.
It sounds like you may have a hardware issue with your MicroZed board. Do you have access to another MicroZed to verify this? Has this MicroZed worked in the past?
If your MicroZed is still under warranty you may want to contact the purchase location for an RMA for replacement.