Unable to install Steam

I am a first time Steam user. I am trying to download client for my Windows 7 machine. However I keep getting this error.

Fatal Error: Steam needs to be online to update. Please confirm your network connection.

I checked Steam forum and as per suggestion given there, I have disabled my Antivirus(AVG), but is it of no use. How can I fix this problem and install Steam?

I believe your problem may be with your antivirus software. Even though you said you disabled it some AV products can still cause issues.

Per this page from Steam Support Programs Which May Interfere with Steam

Anti-Virus Applications - Any Anti-Virus program could potentially block Steam and Steam game access, especially when not properly configured for use with Steam. Please make sure that Steam and all Steam games are listed as exceptions in these programs. If the issue persists, please try disabling or temporarily uninstalling the program to test the issue.

AVG is on the list with the following note:

We recommend that applications listed in bold with a ( * ) symbol are fully uninstalled from your system if disabling them does not resolve the issue

This looks like it may be the solution from the information you have given.

I also suggest checking this list for other programs installed to see if there could be another conflict.