A user can log on to the network but has no internet connection? Explain what could be the problem.

Check that user account is part of appropriate security group
check the proxy settings of the network.

if after checking both doesn't work
try refreshing the group policy and reinstall the client software (browser)

First of all check weather the user account has appropriate membership on the domain to access internet
if that is OK please check the proxy settings of the web browser

if that is OK too try to refresh the group policy of the client and run the login script to make sure all permissions are refreshed .

if after following all these steps no connectivity please reinstall the browser or repair it an restart the PC

First check the user account's membership in AD
if account is allowed to access internet check proxy settings
if proxy settings are all ok update the group policy of the client machine and rerun the login script if does not work reinstall the client software