Can't install Craft on a GoDaddy shared hosting server
Thanks for the advice guys. It's helped me rule out the directories being an issue (sort of). Turns out that I was able to access the files in the craft directory all along. My issue related to the database settings. 

Typically, the 'server' setting in the 'craft/config/db.php' folder is set to 'localhost'. But for GoDaddy you need to use your hostname. Get that by following these instructions.

You will also need to amend your 'craft/config/general.php' settings to include:

'omitScriptNameInUrls' =&gt; false,


At this time, I am unable to get clean-urls working on my Craft install. When 'omitScriptNameInUrls' is set to true, and I try to access any page (besides the homepage), I get that Internal Server Error again. I may open an new question for this as it seems to be slightly unrelated now.