i wanted to install lamp.. but colud not installed it properly somehow.. so trying to remove previous package .. i use purge to remove installed package.. a large number of packege get uninatlled like software centre etc.
when i rebooted my system..it was unable to login to my desktop.. something line running in low graphic mode appeared. i installed gnome desktop. i was able to login to gnome desktop then.. but there was no end to my problem after that..
i am unable to update now and several package are getting installed with errors..W: GPG error: http://dl.google.com stable Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY A040830F7FAC5991
W: GPG error: http://archive.canonical.com precise Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5
W: GPG error: http://archive.getdeb.net precise-getdeb Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY A8A515F046D7E7CF
W: GPG error: http://in.archive.ubuntu.com precise Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5
W: GPG error: http://in.archive.ubuntu.com precise-security Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5
W: GPG error: http://in.archive.ubuntu.com precise-updates Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5
W: GPG error: http://in.archive.ubuntu.com precise-proposed Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5
W: GPG error: http://in.archive.ubuntu.com precise-backports Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 437D05B5 3E5C1192
sudo apt-get update

show us the output of this command.

result of my cat /etc/apt/sources.list query are as follows
# deb cdrom:[Ubuntu 12.04 LTS _Precise Pangolin_ - Release i386 (20120423)]/ precise main restricted

# See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to
# newer versions of the distribution.
deb http://in.archive.ubuntu.com/ubuntu/ precise main restricted
deb-src http://in.archive.ubuntu.com/ubuntu/ precise main restricted

## Major bug fix updates produced after the final release of the
## distribution.

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team. Also, please note that software in universe WILL NOT receive any
## review or updates from the Ubuntu security team.
deb http://in.archive.ubuntu.com/ubuntu/ precise universe
deb-src http://in.archive.ubuntu.com/ubuntu/ precise universe

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team, and may not be under a free licence. Please satisfy yourself as to
## your rights to use the software. Also, please note that software in
## multiverse WILL NOT receive any review or updates from the Ubuntu
## security team.
deb http://in.archive.ubuntu.com/ubuntu/ precise multiverse
deb-src http://in.archive.ubuntu.com/ubuntu/ precise multiverse

## N.B. software from this repository may not have been tested as
## extensively as that contained in the main release, although it includes
## newer versions of some applications which may provide useful features.
## Also, please note that software in backports WILL NOT receive any review
## or updates from the Ubuntu security team.

deb http://in.archive.ubuntu.com/ubuntu/ precise-security main restricted
deb-src http://in.archive.ubuntu.com/ubuntu/ precise-security main restricted
deb http://in.archive.ubuntu.com/ubuntu/ precise-security universe
deb-src http://in.archive.ubuntu.com/ubuntu/ precise-security universe
deb http://in.archive.ubuntu.com/ubuntu/ precise-security multiverse
deb-src http://in.archive.ubuntu.com/ubuntu/ precise-security multiverse

## Uncomment the following two lines to add software from Canonical's
## 'partner' repository.
## This software is not part of Ubuntu, but is offered by Canonical and the
## respective vendors as a service to Ubuntu users.
deb-src http://archive.canonical.com/ubuntu precise partner

## This software is not part of Ubuntu, but is offered by third-party
## developers who want to ship their latest software.
deb http://extras.ubuntu.com/ubuntu precise main
deb-src http://extras.ubuntu.com/ubuntu precise main
deb http://in.archive.ubuntu.com/ubuntu/ precise-updates restricted main multiverse universe
deb http://in.archive.ubuntu.com/ubuntu/ precise-proposed restricted main multiverse universe
deb http://in.archive.ubuntu.com/ubuntu/ precise-backports restricted main multiverse universe

sometime my pc is running very slow after that and some time shutting down automatically.. may it be related to above problems.

I'm sorry, i can't help you. It sounds like you may have removed some core components of your system. I'd back up your important data onto a usb drive and reinstall, but wait till someone more knowledgeable offers you some advice.