Plugin Error "Could Not Create Directory"

I have tried three different plug-ins, all with the same result (all four and five stars). What’s interesting is that earlier in the day, I uploaded a new theme to this new site and didn’t have any issues with adding plug-ins at that time. Then, this afternoon I tried three separate plug-ins, all with the same “could not create directory” result.

Is there an error log somewhere that would provide me with more information about what’s going on? The one I did find didn’t seem to have any related information. I’ve read the various solutions that recommend changing to 777 or 755 etc. but I would like to find the root cause and fix it, not create a workaround.

Thank you in advance for your kind assistance.

A few maybe (maybe not) related topics:

• I am new to WP.
• I uploaded to 3.5.2 today before beginning all of this so it has worked both successfully and unsuccessfully with this version.
• Between the functional and not functional times I did upload a plugin that wasn’t ‘certified’ for this new version, but moments later disabled and deleted it. Could this have ‘broken’ a setting somewhere?
• Another workaround I tried was to upload the files via FTP, and this didn’t work either. I receive the error “550 Can’t change directory to ../plugins/pluginname: No such file or directory”
• I have deleted and re-added the admin user on the database and ensured that it has all permissions but with the same result.
• All folders have 755 permissions with the exception of public_html, which is 750.
• The host is HostGator.
• I come from the tech industry so I’m familiar with troubleshooting in general, but not specifically troubleshooting WordPress.

The temporary site is: http://pediatricsleepconsulting.com/blog/wordpress/?page_id=6668