2004 Prius key issues

I've read through several threads, but couldn't find an answer to my problem.

Here are the details:

My key stopped opening/locking doors (both when in pocket or pressing the key buttons), but still started the car when inside the slot. Changed the battery in the key, it still didn't open/lock doors, but still starts the car when inside slot. It doesn't start the car when not in slot.

Got the second key (with brand new battery) to open and lock the car when I pressed the key buttons. It doesn't recognize the key when it is in my pocket. Again, car only starts with second key in the slot.

I have checked the button under the dashboard and it is in the correct position. 12 v battery was changed in July 2016. The light for "maintenance required" appears when I start the car. Next oil change 1K miles away (99586). Maybe something else needs to be checked? In 14 years, I've only seen that light go on for oil change.

This car was bought new in 2004 and has 98299 miles in it. I love my car and was hoping to drive it to the ground.

Any ideas on what can be the problem? I thank you all in advance for any help I can get.

 

Yes, the button is on. I checked after I read the threads.

 

Will do. Hopefully that is the problem. Thanks so much! Will post here when I find out.

 

An update:
Had the 12 v battery checked and it is fine.
Had an oil change and one of the keys started working normally again (car recognizes the key). Could the oil change have had anything to do with the malfunction of the keys? The other key (new battery) still doesn't work as far as opening/locking doors go, but turns the car on when in the slot.
I'll take the car on Thursday to have it plugged into a computer. Maybe there is something else going on.

 

I guess the "yes" part has to do with the "maintenance required" light and the whatever button/code/witchcraft that made it disappear after the oil change?
And the "no" part with the relation between oil and key?