iPhone iPhone 4 starts then after 5 seconds turns off then automatically starts up again etc

[Iphix]

I just bought a second hand phone off gum tree, it has smashed screen, smashed back glass, faulty home button but lcd still functions i think. so i bought it with a flat battery, then charged it a little, then needed to restore it so i connected it into the computer, held in the power button and home button until the screen went black, then held in the home button until it was in recovery mode, then clicked restore. everything went fine until it was in the "preparing to restore" part of the procedure and the apple symbol came up on the screen then slowly went duller and duller until the screen turned off completely then the apple symbol popped up again then the same thing happened again and again. So this went on for quite some time with itunes still saying "preparing to restore" for longer than usual then error code 1602 popped up saying itunes had an unexpected error and could not restore your iphone. So i decided to do some research and a few people were saying it was the battery and i replaced the battery and the same thing happened. PLEASE HELP!!!