Unplug phone-bat charged-won't stay on

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http://androidforums.com – My phone has the original battery, in good condition, have phone 1 year & 4 months. This is the Epic 4G slide, Gingerbread, non rooted. I noticed at work last night-forgot my charger at work, so used an extra one in the meantime the day before. The battery did die but was able to get it on the spare charger until I could get my original cord. I am noticing it will stay on unplugged if I shut off data or put it in airplane mode. I have thethe phone plugged in now, I also use one of those small fans you can get at W*lm*rt for abot 7-8 dollars, I lean my phone up against it as thi (General)