If it's genuinely a TiVo and not a V6 (Check here if you're not sure) then it doesn't have WiFi and has an inbuilt internet connection.
Regardless, if it's stuck in an update/reboot cycle and won't complete then it has a fault and I'd recommend reporting it.
You can either wait here for staff to pick up, which might take a couple of days) or call in (150 from a VM phone or 0345 4541111 from any other phone) for an immediate response.
It's also worth checking your contract & bills that you're paying for a multi-room subscription, these are normally chargeable and if your extra box isn't activated - that won't be helping.
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