Just an update: I went through a number of recommended steps, and am still having the same issue. Here are the steps I took:
1. Tried disabling all of the plugins by renaming the plugins folder. I checked that all of the plugins did indeed deactivate themselves, but I still got the error message when trying to access the plugins menu.
2. I increased the WP memory limit to 96 and confirmed that the setting took effect by checking in the Woocommerce "System status" section
3. I renamed the .htaccess file. This took the site offline, but did allow me to try to access the plugins page. Still no success.
4. Tried switching to the "Twenty Twelve" theme to rule out the theme (U-design) as the issue. Still no luck.
5. Permalink settings do not appear to have changed since I first configured them.
My next step is to try and check error logs via Godaddy to see if those might tell me something. Is there anything I should look for? Any other suggestions on what to try next?