Probably your best bet is to get it to boot to non-graphical mode and then start playing with your X configuration to come up with something that works. If the system is accessible over a network, ssh in and edit the file /etc/inittab so that you boot non-graphical. You'll want to look toward the top of the file for some lines that looks like:
# Default runlevel. The runlevels used by RHS are:
# 0 - halt (Do NOT set initdefault to this)
# 1 - Single user mode
# 2 - Multiuser, without NFS (The same as 3, if you do not have networking)
# 3 - Full multiuser mode
# 4 - unused
# 5 - X11
# 6 - reboot (Do NOT set initdefault to this)
Your system will have a five on the last line instead of the three, above. If you have a three there, you'll get a text mode login prompt.
If your system isn't accessible from a network, some alternatives are using the Fedora rescue cd (you can download the ISO and burn it from a variety of places that mirror the Fedora distro) or you could probably do the same with something like a Knoppix "live" cd. The rescue cd is probably your best bet since it will mount your existing installation so that you can edit /etc/inittab and then just exit the shell you get to reboot.
Once you get a text mode login you need to figure out how to configure X for your laptop's particular combination of video card and flat panel. The trick is to find out what combinations of refresh rates, etc. work for the flat panel that's attached to your laptop. Hit Google and see if someone already knows the answer.