why won't my iphone backup to the icloud?

I had it checked out at the apple store today. My phone kept crashing at 75% and no one knows why. I was first told to take off all video and extra pics and podcasts to get my "free" up to at least 2 GB. I did that and it kept crashing. I went back the second time to apple store and a scan was done. The guy told me that it is a software issue and I need to back up the phone to the icloud, clear it all off, restore and start over. I was unable to do that. It will not back up to the icloud. So I called them later and asked what else I could do? They first said, drive all the way back (1 hour each way) and they will take another look. So I asked if there was anything I could do at home? He said I could back up to my computer and then restore from there...then go back and back up to the icloud. I restored from computer but it still won't back up to the icloud. I wonder if something was set up wrong for icloud. I remember I had a LOT of trouble setting it up initally...password issues and such. What can I do now? I am out of contract and do not have applecare. Is there a department I can contact or who can help me with this?