Share your experience!
I have been experiencing this for months already. I am honestly not sure how and when this problem started but I am sure that when I bought this phone last March/April 2012, my data network was working. And then an update became available (not the ICS update), problems started to happen. Data network became limited to certain apps only. And then the ICS update happened. 98% if the time, the data network never worked. I only get notifications, for example from Facebook, but when I click on the notification, it always never gets to show me what the notification was about.
I asked my provider about this a couple of times so they can check if their services are running properly and they always confirmed that this service on my account is working well. And I doubt they will disable this or what since I've been using this service since forever! Unless there are any problems with their services, which I am not aware of...
Now, contacting Sony directly seems to be my next (if not my last) best option.
Help, anyone? I'd like to be able to use all features of my phone everywhere and anytime but this problem is preventing me to do so. I love my phone but so far, it's not loving me back. 
Would appreciate any assistance on this.
Thanks.
sorry to hear you have same problems,, I do hope sony would release a fix over these, and there is a good chance they would since you are using their "flagship phone", though it may take long. 
So I tried inserting my sim to an iPhone 4S and my mobile data network DOES WORK! and it's actually fast! Made me more disappointed. 
We need a fix soooon, Sony!
Here's a weird thing that happened to my phone last weekend -- a weird thing that turned out to be a solution!
I borrowed an iPhone 4S to insert my SIM card on so for once I can check if the data connection is really working or not. Turned out, it WAS WORKING and it was pretty fast. That made me even more frustrated with my Xperia. The SIM card from the iPhone 4S, when inserted into my Xperia, didn't allow data connection either. It MUST be really be the phone.
Then as I switched them back, I suddenly received a notification from SMART for new phone configurations - this happened right after I turned on my phone. I figured whenever you insert your SIM to a different phone, it will automatically send you new phone settings. So I accepted and successfully installed these settings (what did I have to lose, I told myself). After this, I tried opening a browser and to my surprise, the page loaded! voila!
So two things I'm considering: Xperia settings from Smart must be wrong and that Xperia should be using the same settings as an iPhone 4S. Settings I received was really for the iPhone 4S.
OR
Smart finally realized that they indeed sent us wrong config settings.
So it's not really the phone, after all?
Hope this helps!
What are the APN settings? Maybe i can change mine manually. don't have a friend who has an Iphone 4S. Can you type in the configuration settings for the APN? Mine shows SEMC GPRS whenever i download the internet settings under Xperia. Thanks!
Already told Smart to send me thr Apple Iphone 4s configuration to my phone but they told me that their technical team will have to send it and gave me a report number for this. Maybe you can type in what appears in your internet settings or APN so i can try to configure it manually? Thanks!
so it was the network's fault, poor xperia.. you blamed him.. lol:smileylaugh: 
Hi farrahvo, try these settings below:
Name: SMART INTERNET
APN: Internet
MCC: 515
MNC: 03
Authentication Type: None
APN Type: default,supl
APN protocol: IPv4
Bearer: Unspecified
All others: not set
Good luck!
Hi there! Good news! My smart data is now working!
What i did was to insert my smart sim to another phone. Tried the data connection using the smart Internet. It was working in the other phone(it was a Nokia phone). It was actually fast as what you've said. Then i returned the Sim to my Xperia S. When i turned the phone on, SMART sent me configuration settings for my phone to which i installed (like you did) and voila! The internet and other applications are now working and very fast too, compared with the GB OS. I tried accessing the browser and i noticed that it has faster response time than before.
So you are right. It's not the phone, its the data configuration settings. Thanks for sharing your advice. Iam now happy!! 
Thank you for the advice and tips on our problems.
i appreciate your taking time out to help us. Finally, our problem is solved.
God bless you!!