Sounds like you have several problems. Contact your systems administrator to see if they can correctly enable relaying from the local host only on the mail server.
Having an open relay will cause your server to be used to relay spam, also, you'll quickly get blacklisted and banned permanently from sending any email to many hosts (especially AOL).
Never have an open relay, even briefly. If you do so, your IP address is toast, and you'll need a new one if you hope to ever send any email ever again.
If you make an email request with a correctly formed, non-forged sender and envelope sender headers, it should be accepted.
Ensure that you're not forging messages, or using a user-supplied address in the "From" or envelope sender fields.
If you are using the IIS MTA, I'm afraid it doesn't make any useful logs (not even optionally).
Mark