I restored from iTunes backup but it goes back to 'welcome to your new iphone'

Question

My iphone 5 was replaced today because of a faulty power button. I had done an iTunes backup this morning, choosing to backup iTunes purchases and the apps as well.
In order to restore the backup to my new phone I had to set it up as a new phone and update to 7.1.2. All good so far.
I then chose to restore from backup (dated today) and it all seemed fine until the restore was complete and the iphone restarted and I was taken back to the 'Welcome to Your New iPhone' screen. Thankfully my photos and contacts have come across but none of my iTunes library, emails or most of my apps. What I'd really like to retrieve are the notes I had in Notemaster...lots of important details about trip bookings, finances etc.
I suspect an incomplete/corrupt backup was made this morning as I think I'd used about 47gb on my phone and the backup file in my application support folder is 11.8gb (although I don't imagine that folder would include all the video & music from my iTunes library??). I thought I could go back to the backup I made in June but it looks like it was overwritten by the new backup I made today...is that right?
Can anyone please suggest a fix or am I going to have to set it up as a new phone in order to get past the 'welcome to your new iphone' screen. First I'd somehow have to back up all my photos and contacts or I'll probably lose them.
Actually, I've just downloaded iBackupBot and I can see all my notes in the backup I made this morning so they do still exist even though the app didn't download in the restore, in fact it looks like a lot of my user app files are there. What do I do now? My head hurts h e l p . . . p l e a s e

Answer 1

I don't think that you need to restore from the backup again. If you see nothing at all in the App Store. Try closing the app completely, reset your iPad and them try again.
In order to close apps in iOS 7, you have to drag the app up from the multitasking display. Double tap the home button and you will see apps lined up going left to right across the screen. Swipe to get to the app that you want to close and then swipe "up" on the app preview thumbnail to close it.
Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.