Iphone 3g shuts down when charged and overheats?

Ok… Well i ordered a galaxy s3 from at&t… And i kinda lost my sim card. -long story…
but i need to find a way to turn on my phone because i have SUPER IMPORTANT info that i need to transfer! And it only turns on for like 10 minutes and then shuts off… Does anyone know how to fix this

i have incredibly important phone numbers and references that i can't get back
its charging right now… IS THERE ANYTHING ELSE TO DO?

Added (1). My phone won't even connect to itunes when it shuts down.
but whenever it turns on it heatsup

Does it overheat when connected to iTunes?

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