I had this problem once and it was quite bizarre. It did not start and there was no lights in the instrument panel. Checked the battery terminals, no sign that it was loose and no foreign stuff on the terminals. I removed the terminals. Cleaned and reinstalled them. It started!!!
On another occassion, there was light on the instrument panel but no clicking noise when turning the ignition. It turned out to be the earthwire even if the earthwire looked solid and secure. With the help of a fellow member, the contacts just needed cleaning but I changed the connector as a precaution.
If the alternator is giving insufficient charge, should the battery warning indicator light up?