I have an old mobile phone (Ericsson T28s).  Yesterday my wife phone me
on it and I couldn't hear her.

It appears that any call made by this phone results in the caller not
being heard.

My immediate conclusion is a  microphone fault.  However when I speak
into the phone I can hear the sound coming back in the earpiece.

Second conclusion is a fault between microphone and modulator in the
phone so sound is reaching earphone but not affecting radio waves

BUT the sound I hear in the earpiece has a slight delay in it.  So I am
thinking the sound must be reaching the network and being re-broadcast
back to me.

So how come the speech can't be heard by someone being called?