car won"t start

I have a Cadillac cts 2006, recently it began to
not start when I go to start it, after trying to start
it a few times, the next time I turn the key it
starts up like it had no problem . It will start up
the next few times then out of the blue it does
the same thing, like the battery is dead, just
clicking, then start up like nothing happened.
Recently while driving it shut down the air
conditioning and the radio and went to battery
saving mode . Replaced battery and terminals,
and alternator, check engine light went off and it
ran good for about 4 days then the engine light
came back on and when I went to start it again I
had the same problem again. Please let me
know if answers for to what the problem is.