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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.
did you bought a micro SIM card or did you cut it? do you have the correct APN settings? go to settings > about phone > status > check the signal
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I have a micro SIM card, of course. 
As for the APN, I downloaded it directly from my provider but let me check again.
ok I would say enter them manually
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Tried looking online for the APN for my network, manually input it but still not working.
Told me to go to sonymobile.com to get the correct settings.
what is your network?
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Smart Communications (Philippines). I currently have the following info/settings from them:
Name: Smart Internet
APN: Internet
Proxy: 010.102.061.046
Port: 8080
MCC: 515
MNC: 03
Authentication type: PAP
APN Type: default,supl
APN Protocol: iPv4
Bearer: Unspecified
All others are blank (showing "not set")
Name: SMART
APN: smart1
Proxy: 10.102.61.46
Port: 8080
Username:
Password:
Server:
MMSC:
MMS Proxy:
MMS Port:
MMS Protocol: WAP 2.0
MCC: 515
MNC: 03
APN type: httpproxy
or
Connect using:
IP address: 10.102.61.46
User id: smartwap
Password: smartwap
Data mode: connection less
Security: On
Show images: On
Response timer: 30
For GSM Data, you will also need the following:
Connection type: Continuous
Connection security: Off
Bearer: Data
Dial-up number: +639198961000
Data call type: ISDN
Data call speed: 9600
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Not working either... 
have you check if your area has 3G coverage?
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