From the Microsoft web site at: http://messenger-support.spaces.live.com/blog/cns!8B3F39C76A8B853F!13931.entry?sa=240159924
If you are encountering the error code 80072745 when you sign into Messenger try the following:
If you are connected to the Internet through a router, remove the connection to the router. Then, directly attach the network or modem cable to the computer. This will help determine whether the issue is related to a firewall setting on the router. Try to sign in to Messenger after you connect to the Internet. If you can connect to Messenger after bypassing your router, the issue may be related to router settings. Try resetting your router (Note: This may revert your settings back to factory default settings and may delete all your custom settings.). Please contact your router manufacturer's Help documentation or customer support channels to determine how to reset your router or enable port 1863 through the router firewall.
If you are signing in from a corporate environment, contact the network administrator to determine whether port 1863 is being blocked inside the network.
If you have Zone Alarm with IM Security installed on the computer, turn off IM Security for Messenger:
Right-click the Zone Alarm icon in the notification area, and then open the Control Center. 3.b.
Click IM Security or click Security to open the IM Security settings window. 3.c.
Click the Main tab or the Status tab. 3.d.
Slide the Protection Level slider to Off to turn off IM Security. Note:
This procedure will change the IM Security settings for any instant messaging programs that are installed on the computer. 3.e.
Sign in to Messenger again to determine whether the issue is resolved. 4.
If you are connecting to the Internet using a Wireless Data card through a mobile phone network, please contact your mobile internet provider to verify if you need to additional data plans that enable you to connect to the Messenger service.