Sorry you're getting these problems, Let's see if we can help you.
I had the issue of my iTunes not detecting my iPad but an uninstall and reinstall fixed that. I see you've done that and the problem still persists though. What version of iTunes do you have? Make sure it is the latest version. What phone and what iOS are you running too? is it Jailbroken?
Have you tried a different cable? It shouldn't make any difference if iTunes is picking the phone up once but it's still worth a try to eliminate any potential variables.
Open iTunes, Go to Preferences > Devices and see what devices you have there. If your phone is there see if you can make a further backup.
Putting iTunes aside for the moment, can you see the phone as a drive when connected and looking in your drive list?