New iPhone is completely dead! (isn't the charger) . - 1

I've been So unfortunate lately. Got a 2nd hand iPhone 3G off ebay last month… Worked for a few weeks then went dead and wouldn't charge. Took it to Apple and they said the battery was completely lifeless so they gave me a new one for £55. Took this phone home, worked for a day, when I woke up in the morning after it had been charging it was completely dead and wouldn't charge. Have tried everything. Have tried restarting it holding both buttons, have bought a new usb cable, i'm losing my patience now. It's a brand new phone! I don't understand it.
What can I do?

The first thing to point out is it is not a brand new phone, its a second hand iphone 3 gs and they are cr*p. The new battery is obviously faulty. If i was you, sell the phone on ebay for more then you payed for it and then get an iphone 4/4s or get an android smart phone. Hope this helps.

Considering it's a 2nd hand phone off eBay which came out numerous years ago, it's a fair chance that something would go wrong with it, I can never trust eBay with second hand electronics.

From what you've said it doesn't seem to be a battery problem so I can only presume it is something wrong with the internal hardware of the phone. Perhaps it is working fine but the screen is broken? Or there may be a problem with the transfer of battery voltage to the phone, I do not know. The only thing you can probably do is get it checked out by an expert, but that will cost more money. Or perhaps you should contact the person you purchased it from off eBay?

You got it second hand! It's not brand new, and it's probably been used! People don't get rid of a good condition phone for nothing, for no reason.
the thing is probably damaged.rather than throwing money at it for new batteries, ask them to check if it's shorting out somewhere.water damage? Bad wiring? Trauma? With any of these, the phone can appear to be totally fine.you're probably better off just replacing it.
sorry about your luck!