I think your phone has a software-problem which has been caused by a virus or an error in the operating software. Try formatting your phone by typing *#7370# in the standby mode and then entering the security code. As formatting clears up the phone-memory, creating a backup of all the important data in it is recommended by Nokia. But, if the problem really has been caused by a virus, doing that might backup the virus too. So, I think it's better not to create a backup (according to your phone's condition).
You can also format your phone by updating the firmware of your phone (visit http://www.nokiausa.com/softwareupdate for information).