Why won't my Iphone 4s show that it's charging when plugged in?

I just recently bought it (unlocked so I can use it for T-Mobile) from a friend of mine and he told me that when you plug it in to the charger it doesn't say it charges but it does actually charge. I plugged it in and like he said, no icon appeared that indicated it was charging. I have to constantly keep checking the percentage to see if it really is charging. I also noticed that it takes forever to fully charge… For example, when I first got it it had about 25% battery. I charged it for the night and in the morning it only had 57%. I used it for a little (texting, facebook, etc.) and the battery immediatley dropped to 20%. Its been charging all day since and at 20 minutes to midnight its only at 56%. Why is this happening and what can I do to fix it? I've used multiple USB cords/outlets/computers and nothing seems to work. I've tried cleaning all the USB's as well.
Is this a problem with the battery itself? If so I don't understand why no device (USB, PC) can recognize when it's plugged in. What can I do to fix this?