A new Clara HD should connect to WiFi. Some of the older devices won't connect after a factory reset as the device connects to a Kobo server upon connection and the original firmware does not support the security protocols now being used. The Clara HD does.
But, the question is what "doesn't connect" means. During the setup, the device will do the following:
- Display the list of available WiFi networks.
- When you choose your network, prompt for the password.
- Connect to the WiFi and get an IP address.
- Once connected to the WiFi, connect to the Kobo server.
Does it do the first two? Does you router show if an IP address has been allocated? Or show the device in the list of connected devices? Can you reach the Kobo server from one of your other devices on the network?
You can try manually installing the updated firmware. I doubt this will solve the WiFi issue, but, there may be a fix for the WiFi included. It would let you use Sideloaded Mode. You can see the list of available firmware versions on
https://wiki.mobileread.com/wiki/Kobo_Firmware_Releases. Just take the latest one.