cygwin - irssi not connecting and screen capturing c-a

"Are you running Windows' (or another) firewall on your system? Have you created exceptions for Irssi in the firewall control panel?
You can always send Emacs a literal C-a by typing Ctrl-A then A. Screen gets the ^A and the following ""a"" tells screen to send ^A to the terminal.
Additionally, there are two ways to change Screen's command character (aka escape character).

One-time use: commandline option
To change the command character for one Screen session, use the -e xy option when starting your screen session. The default is -e^Aa, where x is the command character (^A) and y is the character generating a literal command character (a). If you want your new command character to be ^B, for example, use -e^Bb in your commandline.
Personalized default: ~/.screenrc
To change the command character default, specify it in your ~/.screenrc file. Just add this line to your ~/.screenrc, and your next new session will use the new default command character:

escape ^Bb

This follows the same xy syntax as the commandline option. You can also use the keyword ""defescape"" instead of ""escape""; they are synonymous."