Bad key fob or trunk battery?

I have a 2014 Prius V. I’m unsure if the smart key fob has failed or if the car battery in the trunk (not the hybrid ones) are my problem.

What I have done: when it initially did not start, I didn’t know what to do as a new(er) hybrid owner, so I got a jump. It worked for a number of starts over the next couple of days.

It didn’t start again with the brake depressed and the push start button. It didn’t make the little hum sound I’m accustomed to hearing upon opening the door either.

I fumbled around- unsure what to do and opened and closed the door a couple times trying to figure out what to do. Then I tried again and it started.

I replaced the 1632 battery in the smart fob- thinking maybe the fob just died. The car started a couple of times but is now not turning on after the fob battery is replaced.

I’ve taken it to the auto parts store to see if they could use their diagnostic tool or their alternator health tool on my Prius but they cannot.

There are no lights indicating engine problems and the hybrid battery health indicator looks as it always has- good.

Is there a way to determine if the fob has failed or if it is the trunk battery that needs replaced?