Honestly, I found it silly to show (touch) the fob to the start engine button. Why does it need to touch? nowadays everything is bluetooth or some sort of waves. Bizarre. Thank God nobody noticed me touch the button and speaking to myself.

I have called the tech service too. Waiting for an answrer.
I have been there. I am a victim of the RAV4 dead battery problem. Park the car over night and dead or weak 12 volt battery in the morning. This is documented in battery threads in this forum. OK, the Toyota authorize road service puts a jumper battery on the car, asks you to touch the fob front to the start button and push. It starts right off. OK, in your case the battery may be defective and low so you have to get the fob close to be read or you like me are caught by the dead battery syndrome. Next, if you have a really dead 12 volt battery you may loose your backup guidelines on your backup monitor. If this happens there is a detailed reset procedure to re-establish the guidelines. This needs to be done by your dealer.
OK, if your battery is just defective that is an easy fix. Warrantee your battery.
If you are a member the periodic dead battery crowd, see your dealer and I understand the Toyota now recognizes this problem and has a firmware fix for it. But my concern is why are they still producing vehicles like this, if they know the firmware solution. I have not gotten my RAV4's firmware patched yet, so I can't verify that it fixes the problem.
Hope this helps