First of all, have you switch on the phone yet? The power button for w580i is at the topleft corner (a small black button) at the back of the phone.
To switch on the phone, first slide the phone up, then press the power button till you can sense a vibration, and the startup screen should follow. If the startup screen does not show up, then you should get a replacement from the phone seller at NO COST bcoz the new phone is still under warranty.
Pressing the 'C" button is only for flashing, by putting the phone in flash mode, which you dont need to do. If what you want to do is simply connect your phone to the computer, just plug in the USB cable that comes as your phone accesories, with your phone switch on. you need not press the C button for doing this..
Hope this help you to solve your problem :-)