2008 Tundra won’t start - dash lights shut off when attempting to start

My 2008 Tundra isn’t starting. When the problem first started, I would turn the key and the starter would not activate. I did not hear the starter solenoid clicking either. The Check Engine, VSC, 4HI, and 4LO lights come on. I was able to get the starter to turn and the engine start after several tries of turning the key.

Since then, however, I have not been able to get the starter or solenoid to activate at all. The instrument panel backlight shuts off when I turn the key to the start position. I have to turn the key to off and then back on to get the backlight to come on again. I’ve already fully charged the battery and have tested its output with a simple battery load tester (tests good), so I think I’ve ruled out the battery as a cause.

I would normally suspect the starter to be the issue, but the issue with the instrument panel lights and the lack of solenoid clicking makes me wonder. Any suggestions on what I should check?