How do I use cygwin behind the corporate firewall

Just for the records if you need to authenticate to the Proxy use:

export http_proxy=http://username:password@host:port/

Taken from: http://samueldotj.blogspot.com/2008/06/configuring-cygwin-to-use-proxy-server.html

I doubt that your corporate firewall allows PING, but the others all appear to be one form of http or another. On a Linux system, you can set your HTTP proxy as an environment variable, so in bash, type:

export http_proxy=http://www.myproxy.com:3128

There is a similar environment variable for FTP (ftp_proxy).

Most applications check one of the following environment variables (gem even checks both), so try putting this code in your .bashrc:

proxy=http://host.com:port/
export http_proxy=$proxy
export HTTP_PROXY=$proxy