2002 Mercury Sable won't start as if battery is dead but then starts after 20 minutes

I have been driving this car fine for the past 2 months. but twice it has not started after
driving it 10 minutes and parking it (at the store) the dash lights come on the 1st time I
turn the key but then after that it acts as if the battery is dead and no lights come on
except the "theft" light. the battery is almost new, clean connections. the 'theft" light
will work but nothing else does. after about 20 minutes the car will start and run fine
with no problems...any help is greatly appreciated!!