You can only start the Liberty with a properly programmed key.
Sounds like your key lost its programming.

If the other key doesn't work you may need a new SKIM module.

Same thing happened to me back in 2009.
Quick stop at the dry cleaner. Get back in car and turn key.
Red dot lit on dash, engine cranks but won't start.
Had to have it towed to dealership.
To fix it, dealership had to replace SKIM module and program two new keys.

One of my remote keys died a while back. My symptoms were red light on dash kept flashing. Car would start, run for a couple of seconds then stop. All remote functions worked fine. Turned out to be transponder in key died. Had to call locksmith to program new key since I only had 1 left. I still use remote portion of key to this day. I cut key part of remote off and put it on a letting with new programmed key. Saved me a lot of $$ as remote keys are much more expensive than the keys themselves.

Might be the skim although IIRC:
a. that module is a replaceable part of the BCM so you don't have to do the whole thing. I seem to recall a post with pics on the topic from maybe Sir Sam but unfortunately it was far enough back to be before I was bright enough to start saving that sort of thing.
b. there is an "antenna" wire near where the ignition key goes in that if broken means the system won't pick up the signal from a valid key.

Could be wrong as I'm doing this from distant memory.

IS there any way to disable / eliminate the programmed key. I'd just as soon have a push button starter switch. I always swore I would never have a key that had to be programmed. I've seen to many related problems on all brands of vehicles

Definitely do not need a programmed key, and definitely do not want one.

Just what purpose do these programmed keys serve?

Is there a way to swap them out?

I do not want any

Based on how the computers are linked to the security system, I'm sure it would be impossible to eliminate the key. The programmable key keeps the car from being stolen. I live near Detroit. I'm happy to have it.

With the little bit of research I have done, there seems to be no way to bypass or disable the SKIM. However, there are some technologically advanced car thrives that are able to steal cars equipped with an immobilizer/SKIM.
The way these keys work is there is an RFID tag inside the key. That tag is programmed to work with the SKIM. In order for the car theif to be successful he has to scan the SKIM frequencies and decrypt the RFID code. This can be done with a laptop and a RF analyzer. The laptop would be needed every time the theif wants to start the car or until a legitimate key can be programmed.
There is no way around it. The RFID code is required for starting the car.

Probably the only way for the vehicle owner to by pass this is to disassemble and remove the RFID tag from inside the ignition key. Then glue that tag somewhere near the SKIM antenna on the steering column. As long as the SKIM sees the proper RFID signal, any key that is properly cut can be used to start the car.