My new iPhone won't connect to computer?

I got a brand new iPhone on Saturday and need to connect it to my computer for the first time. When I try it won't show up under devices on iTunes and it won't even show up on my computer. When I plug it in I do hear a small 'bong' which indicates something has been connected but that's it. Nothing else happens. I have made sure my iTunes is on the highest possible software, I have turned it off and restarted both my computer and iPhone. Nothing seems to work. I have been trying for hours, on both Sunday and Monday… What shall I do? Any ideas?

Added (1). I have already set it up by the way, I just need to do something that can't be done without syncing

Any new iphone doesn't need a computer to set up. You can set it up from right on the phone.

Step 1: turn off your phone
step 2: plug in the usb
step 3: hold the power button with the home button (at the same time) for couple of seconds until you see a usb sign on your iphone's screen

then itunes will automatically open and recognize your iphone

Well, that happened to my ipod too. Here is what i did.
I tried connecting it to another computer see if that works. Turns out it works. First i thought it was some kinda virus or something. But days later i was googling and found a solution.

Simply UNPLUG YOUR COMPUTER FROM THE POWER SUPPLY. Yes that's it! Note that this does not mean just turning off your computer because modern computers don't really turn off when you press the power button as the motherboard still gets power.
So first turn off your computer using Shut Down or pressing the power button and then UNPLUG it from the wall outlet. Let it sit for about a minute and then plug it back in.

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