Just to confim a few things.
1. You are on BT Infinity?
2. On the BT Homehub, does the BroadBand light flash orange and then purple or is it not illuminated at all?
3. On the Openreach Modem, does the LAN light flash at all?
The Openreach modem has stickers over LAN2 and the USB connector. They are not used.
The only thing I can suggest is that the openreach modem is faulty on LAN1. If there are no LAN lights flashing (lights next to the port connector itself) on the Openreach modem then it is faulty and you need to have another one installed. You will need to raise this with BT.
You can of course use another VDSL modem. I have used a Draytek2850 and it works very well. It is a combined VDSL modem and Firewall Router. It has 4 gigabit network connectors. Also, it means that you only have one device for Infinity connection instead of two cluttering things up.
There are various models of the Draytek. The basic one that I have does not have wireless. The next two models have Wireless and also the top of the range has VoiceoverIP with connectors for VOIP phones.
Thanks for the reply, after having the kit installed for such a short period of time before it failed I think i will be very seruously considering buying some. Especially when it takes so long to get an some one to send an engineer, and then the wait till the appointment also being very long. If i can find a Draytek 2850, the wireless model for close to £200 i'll pick one up, but i'll still be very disapointed to have been provided with such poor kit in the first palce.