If it is switched off, how do you expect it to receive a signal?
Unfortunately, if you cannot remember where you may have lost your phone, your best option is to have the carrier deactivate the phone and by a replacement iPhone.
In the future, you may want to consider installing a tracking app on your iPhone. Some are free, other requires a subscription. MobileMe is an example of a subscription tracking app exclusively for iPhone. How good is it compared to others? I don't know, I use an Android phone.
Your iPhone (or any smartphone) must be on for any tracking software to work. If it is switched off or the battery dies, then there is no way to locate it
I strongly recommend you to get in touch with a/s service center of Apple company and explains things to them. May be through that way, you may get a clear solution to your problem or perhaps they may suggest you to get a new iphone with a fair discount price.