2002 Buick Century Custom starts when it wants to.

Car was running perfectly fine.  I parked and
went in somewhere 10 mins and when I
came out I opened the door all the lights
came on fine.  I put the key n the ignition and
went to start the car and it kind of grunted at
me as all lights went out. I attempted to
start it again and it did absolutely nothing
not even the random grunt.  I opened the
door there was no dinging or anything and
popped the hood.  I got out my flashlight to
check the battery terminals and everything I
cld think of.  All seemed fine.   Sit down and
call for help outside the car and it amazingly
enuf starts dinging and the lights all kick on,  
on their own.  I try to start it with the same
luck.  It grunts and all dies down.  So
someone tries to jump me.  It seems to b
taking no charge but on the 4th attempt
caught and immediately died back out.  On
the 5th attempt it caught and I drove it home
about 2 miles away.  I shut it off and
immediately turn it back on and it catches.  
The next day the car won't start nor take a
jump.  2 days after that in my attempt to
show someone what it was doing it starts
just fine on the first try.  I take it to the
grocery store and come back and it has not
started sense.  The battery is brand new and
showing full charge.  What could b going
on?