Can you confirm you are able to dns resolve chat.freenode.net? Start > Run:
Code
cmd /k nslookup chat.freenode.net

You can also ping chat.freenode.net?

I'm not sure if your firewall can be queried with PowerShell, but are you sure there's no block on mirc.exe?

Code
Get-NetFirewallProfile -Name Private | Get-NetFirewallRule | Where { $_.Action -eq 'Blocked' -and $_.Name -like '*mIRC*' }


Note: You may also run this with -Name Public

GNU Terry Pratchett - Looking for a mIRC help channel -> Check #mircscripting @ irc.swiftirc.net