What could be the cause of not receiving push notifications through 3g (gsm)? When I'm on wifi I get push notifications normally. But if I go on 3g/4g only, I can use the net normally but I am getting no push notifications.

This is the same for several applications that get push notifications, so it's not an application's fault.

I was reading and there seems to be a single appplication in android that passes the push notifications? I was wondering if maybe that application had background traffic blocked by accident or what other reasons there may be.

If not, what other reason may be causing this?

I have mobile data enabled. Other internet stuff works fine.
My android is: 4.4.2

(this is a recent thing, I dunno what may have changed, but imagine a small child messed with my cellphone, it's possible)
I have found this. A while ago I went overseas and got paranoid and turned a bunch of the background data off in the data usage page. Had a play with it tonight and discovered "Google play services" was restricting. Turned it off and tested it, it seems to work. If you haven't already, try that.