Lots of people having issues with their batterie and push-notifications after „hacktivating“ their iPhones while jailbreaking. The problems are high battery usage and not working push notifications.
This is because the iOS is permanently looking for valid push-certificates. But because you „hacktivated“ your iPhone, there are no valid push-certificates. You need to activate your iPhone via iTunes to get the valid ones.
So what can you do? First you should install SAM. To do this you need to add the source http://repo.bingner.com (need to be insert here -> Cydia -> Manage -> Sources -> Add). After that you should be able to find, download and install it.
Next you need to de“hack“tivate your iPhone with redsn0w. Just hit „jailbreak“ in redsn0w and uncheck all boxes except „deactivate“. After its finished, open SAM.
Hit the „De-Activate iPhone“ button and simply connect your iPhone to iTunes.
If iTunes still says „invalid SIM card“ then you have to manually select your carrier. And also click on an SIM ID even there is only one.