2005 Acura TL. Battery & starter replaced. This morning it would not start, key fob not work. when key turned in ignition, nothing. No lights, radio, click. completely dead. What could the problem be?

Check the battery cables again. Both positive and negative. Check the other ends of them also. Could be a loose connection or bad contact.

Check the starter relay and the starter solenoid on the starter motor.

possible short. backtrack the ignition wiring that you replaced.

Have you done the testing at the starter wiring your not receiving hot to the solenoid circuit on the starter when the key is turned over? Place a test light on the connector for solenoid hot and have some one turn the key if it lights check for constant voltage on the large wire connection from the battery to the starter. If that's all working your starter is bad.

This vehicle is equipped with a chipped ignition system.On your dash warning lights,when turn key into on position you'll notice a yellow key symbal, it should flash then go out. If it flashes then goes to solid on, it means the system does not recognize signal from key. This can be because of wrong key(original valet key will not start car) or key for whatever reason has been deprogrammed. Which can only be done by dealership unfortunately. If system is working(light does go out) then you need to look at possible brake switch sensor,park/neutral safety switch on shifter, and for signal at started when key turned to start position

Do you get warning lights on the dash ?
If yes, a mechanic would check for voltage at the starter.
The circuit between the key switch and the starter has a neutral or clutch safety switch that could have failed.

charge the battery?? or jump the car.. could be a dirty battery connection, not enough power getting to starter

Do you have a keyless entry FOB. If you do replace the battery then program the system. Unlock the doors turn the ignition key to the "ON" position then press either the lock or unlock button of the FOB turn the ignition key off.Now turn the ignition key on again and press either button on the FOB. Turn the ignition off again. Do this 3 times. This initiates programming for the power door locks. Press the lock button of each remote one at a time to be stored in memory. this must be done within 10 seconds of each remote.
3 remotes max. Turn the ignition off and remove the key to complete programming procedure. then test each remote.

You either have bad terminal connections on your battery or the anti-theft system has a system or sencor problem . I would really recomend that honda/acura check your electrical system and anti-theft system

Check the start control signal from the ignition sw to the starter motor.
Check for bad/loose connection at starter motor control terminal.
If there is a start relay, replace it.