Presumably the Chromecast boots OK and you're seeing the "Set me up" screen on the TV/monitor that the Chromecast is connected to?
Within the setup screen on the TV/monitor there's a Wireless SSID in the bottom left corner. On the PC/tablet/phone you're using to setup the Chromecast, does it see the Chromecast SSID that's shown and are you able to run the setup, see the four character code from the Chromecast etc.?
If you're getting as far as the setup, does the Chromecast see the Home Hub SSID such that you can select the SSID you want and allow you to enter the WPA security key?
And which security option is your Home Hub configured for WPA2, WPA or WEP?
I've got two of the older Chromecast and both are connected to Home Hub 5, one to a HH 5A and the other to a HH 5B so the older one's at least definitely work.