Yum cannot damage your system like that unless you configured incompatible repositories and started to upgrade to something which messed up your system. It sounds much as if you interrupted yum during an upgrade.
You need to boot the first installation CD with "linux rescue" and then use the rescue mode's working version of rpm to over-install the rpm package into your mounted system. Use rpm's --root parameter to point rpm to the mount point. If that is not enough of a hint, get back with details in case you have questions.
Once rpm is working again, you can chroot into the mounted system and take a look at: rpm --query --all --last | less
I bet you've upgraded lots of packages and moved your installation into an unusable state.
Btw, Red Hat Linux 7.1 is out-of-date and fully unsupported. The oldest Red Hat Linux which is still supported by
Fedora Legacy is Red Hat Linux 7.3.