It is possible but you need to have a broadband connection...
ftp 21/tcp # File Transfer [Control]
smtp 25/tcp mail # Simple Mail Transfer
http 80/tcp # World Wide Web HTTP
pop3 110/tcp # Post Office Protocol - Version 3
imap 143/tcp imap2 # Internet Message Access Protocol
mysql 3306/tcp # MySQL
your computer should be on all the time..
you need a UPS..
You need to ask your ISP finally for permission..
there is much more and you probably need a backup drive.. all the ports in my prepost need to be accessible (open)...
For the forum, you need to have PHP and MYSQL installed and runing with apache server.. PHP is should be running in "safe mode" to offer PHP executions for outside persons.. FTP and Mail servers are needed too.. Firewall is extremely needed..
If you like to check the functions of Forums, message boards e.g., phpBB, SMS, IPB, Mkportal, PHPNuke... CMS etc. Just download a utility called PHPTriad from download.com, It has php, mysql, cgi.. etc. to run all of common CMSes Offline.
Like Funindia said you can always download webserver packages that come with everything you would need to run a web server. I use Apache2triad It comes with an installer so it does everything for you automatically.