This answer is going to be lengthy...
The TiVo box has an inbuilt internet connection, separate from your home broadband, and it's not uncommon for users to not realise this has failed - which impacts any online functionality.
Look at the "heartbeat" LED on the front-left of your TiVo, this is the status for the inbuilt modem. Does it flash when you have problems? The box is offline if so. TV signals are separate, but anything that uses the internet won't work. Since your homehub doesn't provide the internet for a TiVo, that won't have made the slightest bit of difference.
The newer streaming apps are one of many improvements you'd find with a V6 box - it runs the same software as your TiVo, but on much newer hardware. It has more recording tuners (6 rather than the TiVo's 3) and is much better at using the various streaming services. Crucially it doesn't have an inbuilt modem but does rely on your homehub for the internet.
You've not said what "all possible solutions" are, but if there's a clunking sound that distinctly sounds like the hard drive might be slowly failing - the only fix for that is a box-swap. If you're out of contract and in a position to renegotiate your package, then you're in an ideal position to ask for a V6 swap as part of the deal.
Also be aware of the newer 360 software that VM might offer you - it runs on the same physical box as the V6 but is very different software and has pros & cons. Do your research before accepting 360 as opinions vary wildly, and you can't revert to TiVo/V6 if you don't like it.
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