Your phone should let you do a restore with the computer you last synced it with, and if it was any time recently, you shouldn't lose any of your information/ music/ contacts/ photos, etc.
- Turn off the iPhone (either by holding down the power button, or performing a hard shut-off by holding the home and power button at the same time.)
- Hold down the Home button while connecting to your computer with iTunes already open and ready for a connection.
- iTunes will prompt you to perform a software restore.
- Your iPhone will obviously be wiped new and be reset as a result and you wil have a working iPhone again.
This is only as a last resort and if you have not synced your iPhone recently I would not recommend doing this, however this is a sure fire way to fix this problem.
Really, all a backup does is back up the data for installed applications - for example, it will back up your Tiny Tower saves if you happen to play that. Unless you got all your media from iTunes wirelessly, straight nto your iphone, you shouldn't lose anything permanently.
You might lose your contacts if those aren't set up to sync with itunes. If you have icloud enabled, however you'll be fine.