Unhappy [Q] Phone restarts when it has SIM card. Otherwise works fine!

This Sony Ericsson Live With Walkman was working fine. One day, when on a call, the phone got itself restarted. But after restart, it keeps on restarting as a loop. Thought that it was an issue with bad SIM card. So got a new duplicate SIM card and tried again. But whenever the phone accesses the SIM card or the carrier, it just restarts.

Then tried removing the SIM card and turned on the device. It was working fine. Then set it to Aeroplane Mode and tried putting the SIM. There was no problem. Then when I disabled the Aeroplane Mode, the phone started to restart like a loop! So thought that it was an issue with OS(Gingerbird).

Then tried updating the OS to Sony's ICS update. After that, inserted SIM card. At first time when it is started, it was on Aeroplane Mode(which I enabled earlier). So, when I disabled it, the phone restarted. But after restart, it didn't get in the restart loop! But whenever a call is received, the phone just restarts !

Everything else is working fine! How can I fix this issue? Any help would be highly appreciated.

Thank you