Does it cost money to use iMessage when you don't have texting?

I have an iPhone 4S and normally I have unlimited texting but my parents turned it off because I got in trouble. But I can still iMessage? Does it cost money per text without being connected to Wi-Fi? Or how about when it is connected to Wi-Fi?

IMessage is all free.

Nope, iMessage is completely free (from you're texts). IMessages sent (iMessages are sent to another iDevice only) use internet, so the internet used will come out of your data plan if you are using wireless, but it doesn't come out of your data on Wi-Fi.