hmm

 

Is the immobilizer light flashing?

Does you horn work properly?

 

maybe your starter motor is seized?

 

The battery can be fully charged but still have diminished cranking amps. It's probably a bad battery or starter

 

I would try another battery. See if you can pull one form someone else's car just to test it. Sounds like you have a dead cell and it's no longer powerful enough to run whatever relay is clicking around your fuse box. Might be a bad relay but probably not.