No turning on unless plugged in!

Hi,

I have been given an Iphone to look at by a friend.

It will not turn on when i press the power button but if i plug it in to the wall it powers up to say "Successful update Connect to itunes" when i unplug to connect to Itunes it powers off.

Once connected to my laptop it comes on to the apple logo for a few seconds then turns off then comes back onto the apple logo.

Any one have any ideas?

Thank You