Notifications and Badges

I am having problems with my notifications not working for apps and if the notification works the badge isn't popping up or not popping up the right number of badges. I just recently gotten this phone replaced and still doesn't seem to be working properly. I play a lot of games and I do not know when people play because the notification isn't working or the badge not popping up. Some of the apps are paid apps but I noticed that the free version notifications is working... and some of the free version notification not working. I have contacted the developer and they keep telling me to do the same thing over but doesn't seem to resolve the problems. I have restored the phone back to new and doesn't seem to work. Some of the notifications that work before I got a new replacement is not working now. I do not know what is wrong with the notifications and badges... can anyone help me resolve the problems on how to get my notifications to properly work for my apps. All the settings are correct. This is on a 4S 64 GB phone. I use a windows XP laptop for iTunes. Could there be a glitch in my iTunes or is this phone defective as well? Anyone else have problems with notifications? The paid version games I play is Word with Friends, Scramble With Friends, Hanging With Friends, and Draw Something. Matching with Friends is a free version.. notifications use to work and isn't now. Dice with Friends doesn't pop up the correct badge.... Any suggestions and thoughts would greatly be appreciated. Thanks.