Chosen Solution

The iPhone (8gb, 3G, not jailbroken, unlocked) won’t turn on, i haven’t dropped it or anything, when i try to turn it on it just appears the apple logo for about 30 seconds or so and then it turns off again. when I plug it to the USB connector or charger it happens the same, the silver logo for 30 seconds and turns off. I’ve tried restarting it several times but it does the same everytime.

Sounds unfortunately like a bad logic board, which kinda means you’re screwed, no point in replacing that. You may want to try both resetting and restoring it (if you possibly can) just in case that does something.

Yeah give restoring it a try, if not see if you can still claim a repair/replacement under warranty.