Re: Calendar won't sync, even 3rd party apps.
Well, I can't speak to any issues you may be having stemming from root access, so I'll do the best I can.
1. Are you signed in using the same Gmail account on both the web and the device?
2. Do other Google services sync OK?
3. Have you gone in to your settings to confirm that the calendar sync isn't disabled?
Please hit the "like" button if I've helped.