After letting mIrc have umteen retries, I got a prompt from the help menu, which told me this:
Unable to resolve IRC Server
If you try to connect to a server and see this message, the problem could be:

Your Internet Provider's DNS isn't working
This happens occasionally and is a temporary problem with your Internet Provider. This problem would also result in your being unable to connect to other internet services such as web sites. You should try again later.

An Invalid or Non-working IRC Server address
You might be trying to connect to an IRC Server that is currently not working, or perhaps is an old address and doesn't exist anymore. You should try another IRC Server.

Trying to use the 32bit mIRC with a 16bit winsock
Try the 16bit mIRC to see if that solves the problem.

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If the theory does not conform to the facts, then the facts must be discarded.

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Never argue with an idiot. He'll drag you down to his level, & beat you with experience.