I had a quick look at ChompSMS, and basically it is a service whereby you can send an SMS at low rates via Wi-Fi or using a cellular data connection, Skype has this feature just not for ANDROID at the moment. So when you send an SMS, it's via the internet to chomp and then they forward the SMS at a much reduced cost.
Perhaps this is why your daughter can send an SMS but not receive one? The fact that the stock SMS app isn't there is perhaps not good. I am fairly new to ANDROID, but I do know some apps are needed for basic functions, such as SMS. Even if you don't use the stock app, it's still needed.
If at all possible, you could re-flash (install) Japanese Jelly Fish this would reinstall the OS and any missing apps. I am not sure how much your daughter has personalised her phone, I'm guessing quite a bit. But if you use the Apps2SD feature you could move most of her apps to the SD card, that way when you re-flash you won't lose too many apps.
I hope this is helpful. If you have any questions then please post back.
Edited by Anil k Solanki, 24 May 2011 - 03:27 PM.
Galaxy NEXUS with a side of Jelly Bean.