Watch the $TWIKIROOT/lib/TWiki.cfg file, as well as your VirtualHost configuration in httpd.conf. Both are pretty twitchy.
A few things I'm seeing.
The front page, [link|http://twiki.iwethey.org/|[link|http://twiki.iwethey.org/|http://twiki.iwethey.org/]], has a link, "Get started", that points to [link|http://twiki.iwethey.org/bin/view/Main/WebHome|ttp://twiki.iwethey.org/bin/view/Main/WebHome], when it really wants to point to [link|http://twiki.iwethey.org/twiki/bin/view/Main/WebHome"|[link|http://twiki.iwethey.org/twiki/bin/view/Main/WebHome|http://twiki.iwethe...Main/WebHome]]. Looks to me as if you've got an extra '/twiki' in the actual url, which tells me you've probably misconfigured the VirtualHost in httpd.conf. After setting the value appropriate, restart the webserver ;-)
If not there, then walk through TWiki.cfg and make sure you've got the appropriate values in there. Changes take place immediately, there's no need to restart anything, so playing with values is pretty easy. Some of the paths are filesystem relative, some are server (virtualhost) relative, and the distinction isn't always clear.
If you've enabled authentication (and it appears you have), then take a look at this KB entry at TWiki.org: [link|http://twiki.org/cgi-bin/view/Support/WhereIsTheLoginPage|[link|http://twiki.org/cgi-bin/view/Support/WhereIsTheLoginPage|http://twiki.org/cg...TheLoginPage]]. Note the AllowOverride All directive (httpd.conf) and renaming of "TWikiRegistrationPub" to "TWikiRegistration".