After doing some more research I ended up upgrading Armory on the offline computer to 0.92.3 which solved the problem.
I am now able to sign and broadcast transactions.
For some reason the 0.93.2 Windows 7 installer does not support 32 bit machines (contrary to what is said on Armory's download page).
How did you perform the upgrade? If you connected your offline computer to the internet then basically your bitcoins are hacked and stolen and long gone.
This is a cute meme.
You use a USB drive and download the file to it. Then verify the installer and take it to your offline computer and install. At not point is the offline computer then connected to the internet. This security isn't a meme, it is just security for the paranoid.