Currently Being ModeratedMay 2, 2013 2:02 PM (in response to rathaa)
Here's a helpful article for your first inquiry which should help you troubleshoot the cellular connection:
iPhone: Troubleshooting a cellular data connection
I would follow the steps in order and after each step test to see if the issue is resolved.
For the second inquiry, I would take a look at iPhone: Hardware troubleshooting (http://support.apple.com/kb/ts2802), more specifically the section "Will not turn on, will not turn on unless connected to power, or unexpected power off."