Please have a look at the RELEASE-NOTES-en[.html] file(s) on the first CD or no the DVD, it lists the system requirements like;
This section lists the memory required to install Fedora Core 3.
* Minimum for text-mode: 64MB
* Minimum for graphical: 192MB
* Recommended for graphical: 256MB
So if possible increase the amount of ram on the laptop. Also try using a differnet Window/Desktop Manager other than Gnome or KDE. XFCE4 is included on the installation media for example, or maybe some other one; http://xwinman.org/
In answer to your other question, no an older versions of Fedora have the same memory and other requirements.