Have you tried a known working corded phone in the test point of your main telephone socket?
A very common issue with the old home hub 1 is the failure of the power unit to give the correct voltage. It that is your original one, then you have been very lucky.
I still use the HH1, but have changed the power supply unit twice.
You would be best to ask BT for a replacement, which would be a home hub 4. If you have a spare 9 Volt power supply, you could try that on the home hub 1, make sure you check the polarity.