I've just installed TigerVNC on my Fedora 15 machine from the package manager then in terminal (as root):
chkconfig vncserver on service
vncserver start
None gave me errors, so I went back to the Windows 7 machine and fired up the viewer. But after a few seconds i get
unable to connect to socket: connection timed out(10060)
Does anyone know what to open up or fix on the Fedora machine to make this happen?

iptables -nvL. On Windows, we can't help you. – Gilles Jun 2 '11 at 18:47