Thanks, guys, I understood some of those words! Looks like I've got some reading ahead of me. What I don't understand, though, is what changed such that the folder had to be changed from 755 to 777? Everything was working perfectly until (presumably) both myself and the other ModX user were working on the site at the same time.
Maybe the host uninstalled or misconfigured suExec or suPHP?
MODX-friendly hosts:
http://bobsguides.com/modx-friendly-hosts.html 
