Well Alby, I really appreciate your answer, and it certainly was thorough. But here are the problems I ran into while trying it out:
1) although that folder exists for me, vhost.conf doesn't exist. The only 3 files in the folder are httpd.include httpd.include.new and webalizer.conf -- so running pico (i actually used vi) just created a new file, vhost.conf. I put in the configuration settings you recommended and saved it. Didn't fix anything.
2) I tried modifying it with things like removing "/httpdocs" from the string, since I'm trying to get to domainroot/secure_includes but that didn't help
3) I tried following the advice on this page but also, didn't help. Still getting the warning:
Warning: main(): open_basedir restriction in effect. File(../secure_includes/dbcnx.php) is not within the allowed path(s): (/usr/local/psa/home/vhosts/domain.com/httpdocs:/tmp) in /usr/local/psa/home/vhosts/domain.com/httpdocs/login.php on line 3
I assume I have to find the place where that value is set. I just don't know how...
Again, thanks a ton for the response, though.