New Battery...Still No Start

[Maggie May]

Hi everyone. I'm new to riding so there could (and hopefully is) a very simple solution to my problem here. Please, feel free to point out the obvious. I bought the bike used about a week ago, and was told that it had excessive valve noise and needed top end work. The guy I bought it from said it needed to be jumped each time it was started so it would definitely need a new battery. Jumped, it would start, but once the engine cut off, it was back to stage A. Jump, ride, die. It was still a great deal on an '01 bike so I got it anyways.
After getting it home, it seemed the first thing to do was to get a new battery. After putting in the battery it ran for about half an hour before the lights dimmed and it quit. So, I got a battery charger. The guy at the shop only charged it for half an hour. I left it on the charger overnight to ensure a full charge, and Success! That morning it did start right up.
Until the next day.
I assumed since it started the day before no problem, that it would start up fine today, but the starter seems to click, click, click...nothing. Until there are fewer and fewer clicks and the poor thing just won't respond.
This is my first bike, and I know about zero, other than how to ride it, so any info will be helpful.
Thanks,
Maggie