Hmm, it looks like it is trying to connect to an ADSL signal rather than VDSL. I assume you do have an Infinity connection and not ordinary broadband. If you haven't already done so, try a full factory reset and then try setting it up again.
Just to make sure your line is working properly, is it possible to try a neighbours Home Hub. Just seems a bit co-incidental that your modem stopped working and the Billion won't either, albeit with different symptoms.
can you check there is a dialtone with a phone please
a landline handset is a must really and only costs about £5 you could be trying all this effort and problem is no landline or a landline with a great deal of noise. ypou don't have to use the landline but a phone to check the line is virtually essential. it is also a good way to check your line an avoid an openreach callout charge of £120