Welcome to Android Central! Is this the Verizon Droid Mini, or is it some other "Mini' phone, like the Samsung Galaxy S4 Mini?
In this case, you might have to clear the data from the launcher, which will wipe your homescreens and require you to set them back up again. Go to Settings>Apps>All, select Launcher (or it might be Home, or something similar), and Clear Cache/Clear Data. Now set up your homescreens again to your preference, and see if the unread count badge works again.