I decided to go with CDOSYS since it was already installed.
I forgot that I had to specify a smtp server and surprisingly it gave no errors when I sent an e-mail from the forum!!!
The only reason why I figured out e-mail wasn't going out was I was no longer receiving any e-mail from the forum (i.e. topic subscriptions). The forum "pretended" to send the e-mail even though it wasn't. Luckily I was extensively testing it after moving to the new server otherwise I might not have noticed for awhile.
Also, CDOSYS turned out to be better since we turned off the built-in SMTP server in IIS and went with a different mail server software on the same server (for the time being). CDONTS and the other mail server can't run on the same server at the same time (port conflict). But CDOSYS works just fine.
Thanks for answering my questions. 