IPhone 3GS Battery Problems?

In april this year my IPhone 3GS has been randomly turning off when i do multiple thing and when I try and turn it on, it won't really turn on without it being plugged into the charger. I forgot to mention about 1wk before this started happening, i dropped my IPhone and it only has a little crack on the top left corner.
This problem has been really annoying me so I went into Apple at Carindale and told them about my situation. They said that I would need to backup and update the phone to see if that would work.

So this morning I did the update with no problems and it started working normally. 2 hours after using the phone after the update my phone was still on 100% battery life. I thought that was a little bit weird because i was using facebook, instagram and games and I thought the battery percentage would be down to about 70%.So I turned off the IPhone and see what would happen when I try and turn it on. Half way when I was turning it on, it decides to turn off. I plug it into the charger and It decides to turn on. Then I discovered something. When I turned it off, it was 100% but when I turned it back on it was down to 82% means it's not showing on my IPhone the right percentage, its just showing the percentage when it as lastly changed and it would stay at that percentage. I went online to see if anyone had the same problem and I found someone saying to reset your settings in the ph, so I did that and it has kinda been ok so far, but just had one turn off.

Just before I started typing thi question, I turn it off and back on and see what happens, I had no problems and now the battery percentage is starting to down but really slowly. But i'm not too sure if it will be like this for long.

What do I do? Is there anything else I could do? I was thinking of taking it into apple once again or maybe get a new IPhone 3GS battery.

As you have already updated your iPhone that means no software problems! But as you have dropped it, i think it must be some hardware problem in the battery and the stuff related to it.
ADVICE- Why won't you check the hardware at the apple service center.

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