If after performing a system restore, many of the Apps on the Start page won’t open, and you’re getting the error message “Your Developer’s License has Expired. To Continue to use this App, Please Renew your License”, there’s 2 techniques that can work for you.
Technique 1: Reinstall each app individually.
This could take a while, and unless it’s just a single app, this likely isn’t the easiest way to approach the problem.
Technique 2: Sync your app licenses.
The full details are here, http://windows.microsoft.com/en-US/windows-8/what-troubleshoot-problems-app, but I’ll include a summary.
On the Start screen, find the Store app to open the Windows Store.
Swipe in from the right edge of the screen, and then tap Settings.
(If you’re using a mouse, point to the upper-right or lower-left corners of the screen, move the mouse pointer, and then click Settings.)
Tap or click App updates. If you haven’t signed in to the Windows Store, sign in using your Microsoft account.
Tap or click Sync licenses.
Once your app is either reinstalled or the license is synced, it should start to work again normally.