Download yum as an RPM package and install it like 'rpm -Uvh yum<version-name>rpm'. Then you have yum again.
Opposing some of the comments - upgrading to recent Fedora version is not necessarily the best idea for older PC's. If it runs as a server without X.org and upgraded with yum, then only the core system is updated, which is OK. But if you have Gnome or KDE and get the newest versions on old machines, then X-sessions will be a drag.
The usual argument for recent Fedora's is security, but given the fact that Fedora is the bleeding part of RedHat's development, you will rather get security flaws or bugs - best example was Fedora 10 and it's stupid bugs in the network GUI code on the initial installer release.