[exim] Exim not authenticating with auth-requiring server

Hello exim community,

I'm frustrated trying to make exim work for at least four lengthy hours and
still no glory...
You see, I want to configure it as a forwarding MTA to my ISP smtp server,
but my ISP requires that I authenticate.

My goal is to have a non-authenticating SMTP on localhost so my applications
can use it.

I was followed the steps that "dpkg-reconfigure exim4-conf" brought and then
added a "*:user:pass" to the client.passwd file. Later I updated the
configuration, but nothing yet.
By the logs I can see that my server is saying that no authentication was
done, but I can't actually check the exim commands sent via SMTP.

So to wrap it up:

1) Does anyone know what's going on??? Why exim won't authenticate to my
lovely ISP SMTP server?

2) Is there any way a human can tell exim to please log the SMTP
conversation somewhere so I can take a peek at it?

Thanks for anyone that helps me keep my sanity (and hair) by shining light
to this problem.

Yours,
Rodrigo Madera