I recently have attempted to reinstall openSUSE 13.1 64-bit on an Dell Inspiron 620, and after each of the 2 or 3 installations, my package management programs have all frozen as soon as I have opened them. I have tried installing on different hard disks to rule out any remote possibility of hard drive failure, and tried installing with both a KDE Live DVD and the install DVD, both of which have passed media checks. The openSUSE 13.1 installation I had before worked perfectly fine, and the openSUSE 13.1 64-bit installations on my other computers still work fine.
Is there any way to get my computer to update and add packages again?

use the terminal
you will then see the error

likely it is looking for the install dvd
not a common error with suse ( very common for fedora) but can happen

In my case, it was looking for the online repos. When I re-figure out ndiswrapper, I'll re-enable those repos. Thanks!

It allows me to install packages and run zypper up when I disable the update repos, but when I add them back in, zypper returns to freezing up after saying "Reading installed packages" and YaST2 software module freezes upon startup.

why do you need "ndiswrapper"
for what hardware is it that you MUST use the Microsoft XP driver for it
yes XP only drivers

the suse docs
http://en.opensuse.org/SDB:Ndiswrapper

My wireless network card - when it uses the driver that comes with openSUSE and Fedora it spontaneously works and stops working. For some reason, the XP driver has made it work consistently. I don't have this issue with recent versions of Ubuntu and Linux Mint.

I got the web acting right, and after fiddling with the repo settings, I got the update repos to work. Thanks for the tips that lead me to an answer.