Plug it in to a Mac and download coconut battery (Mac app). That will tell you how fucked your battery is.
Cheers - will try this now.
Edit - Coconut battery says it can't find an iOS device, even though my device is plugged in on iTunes and trusts the computer.
I'd take it to apple. Sounds like a fucked battery.
@kimchi started
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Plug it in to a Mac and download coconut battery (Mac app). That will tell you how fucked your battery is.