iphone 3g 16gb faulty *

The phone was working then stopped powering up with out a lead in from the mains. It would just flash on and off when connected to a pc. I have tested the phone in the mains and the apple logo comes on then around ten seconds later switches back off. I had managed to get it on with the itunes logo but when you pull out the mains lead it turns straight off. I aquired this phone through a joblot that I got from auction,and although I am no expert on these phones,I have a funny feeling it may need a new battery. The back cover shows minor wear and tear althogh overall the phone is in good condition. Cash on collection is prefererred and is sold as seen with no returns as I have clearly stated it is faulty. Thankyou