iTunes and iphonenot synching, device not on the list in preferences.

So, let me make sure I understand you correctly. You are connecting the iPhone to the computer and are trying to do a backup using iTunes? However, you are not seeing the icon in iTunes to select the iPhone? Are you using a PC or a Mac? Do you have the latest version of iTunes?

If I'm correct, see if the information here helps, Back up your iPhone, iPad, or iPod touch in iTunes on PC - Apple Support

If you go to Preferences and Devices in iTunes, the only thing listed there is the backups you have done on the device. Your iPhone will not appear there if you have not done a backup of the device on that computer. You should click on the iPhone icon to see if it will open in iTunes. If you try to create a backup, what exactly happens? What are you seeing on the screen?