How to backup or sync a jailbroken iphone?

I recently jailbroke my phone and since then I have been unable to sync or back up my iPhone using icloud or itunes. I'm trying to switch to a new phone and I can't transfer my data from my old phone without backing it up. I have watched countless videos and tried everything I can think of. I need help! Please and Thank you

Added (1). Everytime I connect the thing to iTunes it says an error occurred and it can't sync or backup.

(I'm obviously smart enough to jailbreak my phone so please don't provide obvious answers like plug it in to your computer or reboot)

Http://lifehacker.com/5986654/how-to-backup-your-cydia-downloads-before-upgrading-ios

Connect it to iTunes

Reinstall iTunes on your computer or if you want to backup Cydia apps (tweaks), install openBackup from Cydia.
Please choose as best answer if helped.