Can I open a fresh iTunes account

I ticked the box marked encrpyt when backing up my iphone on to itunes and I have run into the random password situation. I have tried loads of passwords, changed my passwor. I set-up a keychain to try to view the password but after I had checked back on these support pages I found out I could not view the keychain anyway on my phone.

I turned of the keychain and then set up again with a new password and redid everything again and reset the folders etc but still no luck.

I have backed up to icloud and reset the phone as a new device and then restored from icloud. I've deleted the itunes back-up but I am still unable to make another iTunes back up without the password even though there is no existing back-up now on the computer.

Everything I try to do the computer keeps asking for the password and I have no idea what it could possibly be. I didn't set one. I have tried lots of the suggestions on the support pages about dropping numbers and changing uppercase letters, using spaces and the $ sign and I can't think of anything else to do now apart from start again with another account. I have looked at the idea of deauthorizing and reauthorizing the computers but I'm not sure whether the password will still be on the computer if I reauthorize it.

I need to back up to itunes to use some software. So I figured it might be easier to start all over again with a new account but I am not sure if that is against the rules or not or if the IP address of the computers means that the password will reassign itself to the new account anyway.

Big Thanks shout out for my last answer. It saved me hours of time by stopping me going down a blind alley.

I would really, really appreciate any other ideas or help anyone may have.

Thank you.