How to upgrade jailbroken iPhone 4 with iOS 6.1.3 to iOS 7.0.4? I bought an iPhone 4 online around a year ago, maybe more, without knowing it was jailbroken (I should have sensed this by the price, indeed too good to be true).

When I tried doing the upgrade everything got wiped out and I had to use RedSnow to restore the newest version at that moment. This was iOS 6.1.3 which was decent — I could use almost everything except making phone calls.

Now a few apps are requiring me to download the newest version of iOS in order to operate properly. The next iOS version that appears suggested is 7.0.4. I have backed up all of my information on both the computer and cloud.
Restore the device with iTunes (connect the device and click Restore in iTunes).  
Once the device is restored, set up the device using an iTunes backup and select the iTunes backup that you made before you restored the device.
If you want the device jailbroken, jailbreak the device using evasi0n 7.