For this endeavour you will need the package named Lynx (you can also use Curl, but since I have never worked with it…..).
It will work only for machines which are directly on Internet, but you can trick it by setting environment proxy variable :
# export http_proxy=’http://10.10.10.96:1234′
# export https_proxy=’http://10.10.10.96:1234′
# lynx www.google.com
Note that the speed is much less than with ordinary browser (!), but it does not matter since it is a diagnostic tool.