It sounds like you have two separate issues.
1) mIRC won't install. This probably is related to anti-virus. You've already mentioned that AV has blocked at least one other problem from installing, so it's entirely feasible it is blocking mIRC too. Disable it temporarily and try again.
2) You are unable to connect to servers. This is likely a firewall issue. Disable your Windows firewall and AV firewall (again,
temporarily) to confirm this. You mentioned you could not figure out how to disable your firewall. It's explained here:
http://windows.microsoft.com/en-us/windo...f=windows-vistaManaging your anti-virus and/or firewall are likely out of scope of mIRC support. Although someone might chime in with extra info, you're probably better off asking a question like "how do I temporarily disable ____" in the respective support forums for your anti-virus and firewall. You're more likely to get a proper response there. All information seems to indicate this is an issue with other software on your system and not mIRC.