Some time you experience ping is not working and no browsing when you visit some wesbite but skype is still running.

That might be due to incorrect resolv.conf file.
To resolve the issue search for backup resolv.conf file and replace it or create a new one

# rm /etc/resolv.conf
# cp /etc/resolv.backup.conf /etc/resolv.conf

if you don’t have backup file then its ok, reset your network and connect again, it will be automatically created for you.