I installed the half-life patch as suggested and Half-life is working now. For counter strike, I phoned up Sierra Support and they have solved my problem. The problem was with Zonealarm firewall. I had to shut-down the firewall to play, even though I gave CS permission to access the internet through Zonealarm etc.
Installed Sygate yesterday and have had no probs running it with CS.
Thanks again for the help!