I think that iTunes keeps track of the last backup even if you delete it, whereas your device wouldn't - but not really sure about that....but once you get a new one up to iCloud they should be in sync.
Try signing out of iCloud on your device, then sign back in again, and try your Backup Now again to see if it will back up. Let it just go, and go do something else. It is always a good idea to hook it up to power when backing up. If it thinks you have no previous back up, then it is going to back up the entire device, which can take some time. After the first one, it backs up only the info that has changed, so subsequent backups take a lot less time.
You can also turn on Automatic iCloud backups by going to Settings>iCloud>Backup - make sure that iCloud Backup is turned on. Then plug your device into a power source, make sure it is connected to Wifi, and then let it go to the Lock Screen (sometimes best to do this when you go to bed for the night). In the morning, see if it backed up during the night.
With automatic backups, iCloud will back up your device once during each 24 hour period. As long as you have it connected to power and Wifi and you have the Lock Screen on.
If that also does not back up your device, then you may need to contact iCloud support. But give these options a try, and don't be a helicopter parent. Get it started, and walk away. Your devices like a little privacy when they are backing up. Too much pressure and they just wilt.... š
Cheers,
GB