2005 Buick century battery problem????

Ok so rewinding the the summer time, my car
would sometimes crank a little extra before
starting. Once it didnt even crank at all but after a
few tries it finally cranked and started. When winter
hit, I was told I had a bad battery (had to jump it
one cold morning, and then replaced it). That was
back in october. This week it did the same no
crank thing when I went to start it after driving it for
a while. Once again it started up after a few tries. A
few times a day when I start the car it just cranks
and crank until I have to turn it off and restart it.
Sometimes it’ll turn over and keep running other
times I have to crank and crank again. This
morning (mild day not cold at all) it cranked and
cranked but didn’t start. I went to restart it and it
will not crank AT ALL and all the lights in my car go
out. But after it sits for about 10 mins, the lights
will start working again (almost as if the battery
recharged its self??) but it won’t crank and the the
lights die out again. It won’t even start with a jump,
it’ll get some juice but then will go dark again even
with the jumper cables attached. Is it the battery or
the starter that has drained the battery?? No
battery light on dash.