How can I fix or troubleshoot my Internet connection problem? I am using a Sony Ericsson Xperia running Android 2.3.4. When I try to access online applications like Gmail, Facebook, Android Market etc. I get an error that says No connection, retry? or No data service provider.

How can I overcome this problem?
Make sure this isn't a DNS issue.  In the browser try navigating to the website by its IP address as opposed to the name.

On your computer open command prompt and type in ping google.com and press enter.  The 4 numbers 1-3 digits long separated by dots is the IP address (e.g. 74.125.113.106).  Now on the phone open up the browser, and in the  navigation bar type in "http://" followed by the IP address you got from your computer (e.g. http://74.125.113.106) and press the Go key.  If the website loads - your phone has a bad DNS entry.  The Market has several apps for changing phone's default DNS.