Battery does not charge (displays battery/plug icon on top right)

Question

iphone 4 is about 3-4 months old
Symptoms:
phone started to have issues a few weeks ago
it does not seem to want to charge
when plugged in, it displays the plugged in icon but doesn't seem to charge
have tried various charges (usb AND wall) and it won't always charge
the same charger that works, also might not work
few weeks ago, phone was down (out of battery for about 4 days) and then all of a sudden decided to charge
yesterday, it was plugged in overnight and it did not charge at all. but it had about 15% power left, so when i looked at the icon on the top right, it had the battery with a plug icon (i think that means its indicating the battery is fully charged) so it wouldn't charge at all
then i tried 3 different wall charges and one of them changed it to battery with a lightning bolt. then it started charging
so it seems like somehow the battery thinks its charged and does not charge even though its not really charged.
Could this indicate a problem with the battery, or the phone?

Answer 1

thanks, will do..
Only problem i have is that the issue is intermittent, and dealing with mechanics and even computer shops if they can't replicate the problem they can't fix it.
the last time i had made an appt with apple store, the first time i ran across this issue, the phone started working the night before i had to go to the store.
whats the remedy in this case? as far as replicating the issue or trying to show them the issue.. haven't dealt with the apple store for warranty before so i wanna make sure i can explain the issue to them and not getting told that they can't do anything because they can't replicate the problem.
I will take a look at the pins tonight when i get home, i've been using a loaner phone since the iphone4 has been somewhat unreliable in the past few weeks.