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Try a factory reset of the Homehub by pressing a pin into the recess button on the rear for about 20 seconds. This can often sort out problems.
It may well be that you do have a faulty Hub and that it needs replaced. I would suggest that if possible you stop resetting it as that could cause further problems.
Meanwhile you should contact BT Customer Services and report a fault to them and request another hub.
I would not mention that you suspect it may have been damaged by a power cut as they mean deem that is "your problem" and not BT's and only offer to replace it for a fee.