I have attempted to install FC4 many times on my PC. I finally got it to fully install without hanging up on something. It is the 64 bit edition and I selected "entire package" to install.

The following problems occur (after install)
:when the sys is booting, I notice an error message that says:
"PCI can't allocate resource region 0 of device 0000.03.00.0"

:it continues to say this and when the "text phase" of the booting process was done and it went to the graphical part, it would freeze if I moved the mouse (after about 5 seconds of movement)

The first time I tried to log into my new install, I entered my username and password and it went to the next screen and froze. I rebooted and tried logging on as Root instead of my username. Same thing, it went to the next screen and just froze. No little icons came up to show me that services were loading. I rebooted and tried loggin on with my username again and this time it went to the next screen and icons popped up and services began to load.

Now it just gets stuck at "Red Hat Network Monitor" on bothe my user name and Root. I tried a different interface "KDE" and it just showed a blue screen.

I can log in for a terminal session but don't know how to fix any of these problems. Any suggestions?

If you can open a terminal session, check the log files for any error messages.
Plus you can kill X a few times until it disables itself until you reconfigure it.
You could also remove the mouse and reboot.
When kudzu pops up after checking for hardware changes, have it unconfigure the mouse. Try running gdm after you log into the terminal. This should start the configuration for gnome desktop and X.
Fedora works with USB mice as well.
Its also possible that some service is hanging and preventing the desktop load.
At a terminal you can disable the service from startup using
chkconfig --list
chkconfig --levels 0123456 service off
I would start with the Redhat Network Monitor

Hope this helps