'Connection refused' is a TCP/IP error, not a sendmail error. It means you are attempting to connect to a port where there is no server running. Make sure that there is actually a sendmail daemon running on whatever localhost.nycap.rr.com translates to (probably the machine you are running your script on) and that it is running in server mode.
If this were a relaying problem, he'd be getting something like 'relay denied', not 'connection refused'. He hasn't even established a connection to sendmail. Relaying has not yet come into play here.
How are you sending the mail? Are you piping to sendmail or mail? Are you using modules? Your original note was light on details.
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print map { my ($m)=1<<hex($_)&11?' ':'';
$m.=substr('AHJPacehklnorstu',hex($_),1) }
split //,'2fde0abe76c36c914586c';