Do I have a battery problem?

I had a very strange occurrence two days ago with my 2011 gmc Yukon XL/Denali.
My wife and I go to the Sonic drive-in for a burger. It was mid day so no interior lights were on, and the radio was off. We were there for 20 minutes. Time to leave-I turned
on the ignition, twisted the key to “start” and NOTHING not even a click. No dash lights, no interior lights, nothing but the “check engine icon” on the dash. I took the shift lever out of park and back in again-fooled with it for 10 minutes. Still no response from the battery. New Energizer battery (730 CCA) was installed Jan 2014. Finally got a jump start. Borrowed jumper cables (small gauge wire) resulted in a slow charge which took 20 minutes before engine would start. (Tried every 5 minutes until success) Drove 1/2 mile to home, with engine running voltage at battery measured 14.4 volts. Turned engine off- voltage at battery - 12.22 v.
Do I have a battery problem or could it be something else.