Broken kernel after cleaning up grub

I used uname -a; lsb_release -a; dpkg -l | grep linux-image to search for old Linux images. Then I used sudo dpkg -P to remove those older images and cleaned up grub with sudo apt-get --purge autoremove and sudo apt-get clean . I had left the ii linux-image-3.0.0-12-generic 3.0.0-12.20 Linux kernel image for version 3.0.0 on x86/x86_64 as my only choice in the grub menu.
On trying to reboot an error message showed that the kernel was broken and the system would only boot from the Live CD. Then I reinstalled Oneiric alongside because this option offered retaining all documents, etc. However, I seem to have lost my documents and previous programs and cannot connect to the internet. My broadband network connection is accessible only with the trial of Oneric from the live CD. Now the information in the Network Connection dialog box does not show my existing wireless connection, instead it showed a wired connection although I only subscribe to a wireless broadband connection. I have repeatedly deleted the wired connection, which reappears of its own.

Kindly advise if it is possible to recover my lost documents and programs, if possible.
I am most grateful for your kind help – thanks again