For 1.013 I performed a fresh install of the game, so I downloaded the full 1.013 installer from download location #1 (FileFront) listed here:
http://www.arcengames.com/aiwar_buy.php. The installer ran part way through, then complained about data1.cab being a corrupt file. I tried it again, then rebooted and tried it a third time, but still no luck. Guessing that the download might have been corrupted, I tried downloading it from download location #2 (GamersHell) and got the exact same error upon installation. Finally, I downloaded 1.010 from download location #4 (AusGamers) which installed just fine. From there, I used the internal patcher to get it up to 1.013.
I'm not sure if there's an issue with the 1.013 installer, or if something changed between the 1.010 and 1.013 installers that my computer doesn't like. However, in case anyone else runs into this same problem, that's what I did to work around it.