Verifying the differences between TCP and UDP locally: Interpreting connection refusal and timeouts

When someone says "it won't connect," what do you ask back?A common report of an issue is a sentence like this.I can't ...
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Can a TCP connection be made without an open port?

I've read that there is an "application" that allows computers to communicate without exposing or opening ports to the Internet. Is this possible, and if so, will it create a safer Internet ...