Debugging sendmail – dsn=5.0.0

I'm going out on a bit of a limb here, but I think the problem is your remote host ...

getmxrr(smtp-server.nycap.rr.com, droplocalhost=1)
getmxrr: res_search(smtp-server.nycap.rr.com) failed (errno=110, h_errno=2)
<zeno@biyg.net>... Deferred: Name server: smtp-server.nycap.rr.com: host name lookup failure

It looks like res_search is the culprit here and what it's searching for (smtp-server.nycap.rr.com) is producing the error. According to netdb.h (I think) that error is either non-authoritative host or SRVFAIL.

Checking dns, it does look like something's wrong with that host (please forgive the use of nslookup) :

Non-authoritative answer:
Name:   smtp-server.nycap.rr.com
Address: 75.180.132.33

nslookup
> set q=ptr
> 75.180.132.33

Non-authoritative answer:
33.132.180.75.in-addr.arpa      name = cdptpa-omtalb.mail.rr.com.

I want to say it looks like a forward/reverse mismatch, but I could be wrong. It could just be one bad entry in their mailcluster. I'm thinking the reason that it works in the debug mode is that ruleset 3 is skipped and part of that ruleset is doing reverse lookups on the destination mailserver.

You might be able to solve this with a mailertable, that would go a ways towards fingering DNS info as the culprit. Take a look at this -- Solving hostname lookup failures in sendmail

The log entry

stat=Sent ( <remote-id> Queued mail for delivery)

indicates that the remote server accepted the message. From the perspective of your SMTP server is has been delivered. It is now in the next hop towards the recipients INBOX.

What happens from there is no longer your mailserver's responsibility and neither something you can easily debug from your end, if at all. But typically the message will move through SPAM and anti-virus filters etc. before ending up either in the recipient's INBOX, Spam folder or possibly silently discarded.

Ask the recipient to check their spam folder and if found there have them forward the message headers to you is one approach. Please also read the canonical Q&A's on preventing email getting marked as spam and Fighting spam, what can I do?