In addition, if you have set the firewall option in mIRC, file/option/connect/firewall, try changing it to NONE as odds are you dont have the type of firewall that needs it set to anything else. If you dont see the word NONE when you click on the small upside down triangle/arrow there, leave your cursor in that box and use your up/down arrow keys on your keyboard.
As the others have said, you will need to go into your firewall settings and tell it to allow mIRC and the needed ports access. Usual server ports are 6660-6669, 7000-7001, 113
