Chosen Solution
I have replaced the front display of this iPhone 4 and now it is not working. It will not charge and as I brought this on ebay, I have no previous history. I have used a multi meter on the battery port and this shows no continuous circuit. However, is this just a case of replacing the logic board and if so, why does the Europe shop not sell any (lol)? Is there anything else I can check or do? Update (08/02/2016) I have further tested the l3 and l4 power fuses on the logic board (below the dock connector) and one of them has a continuous circuit and the other has not. So I guess I need a new board.
sound like you have been mugged over by the seller on ebay. i would either get the fuse repaired or buy another defect phone from ebay ( checking out the buyer rating etc ) and then replace mainboard