Andrew: I got the developer tools to function and it does provide a lot of information. My issue, it seems, is restricted to the local server. I have a base map (satellite image) that is being accessed through ArcGIS Online, and this seems to work well. Anything on our local server is being blocked (I'm guessing); hence, anything on Portal and ArcGIS for Server is not being accessed by Firefox.
Our IT department did say that certificates could be an issue, but they wouldn't elaborate more than that at the moment. I'm waiting for our IT manager to return from vacation (should be today or tomorrow) and I can talk to him more about certificates as he's the one who acquired what we're using here for Portal.
The first error message I came across before reviewing the Network status was:
Cross-Origin Request Blocked: The Same Origin Policy disallows reading the remote resource at https://www.google.com/_/og/promos/z. (Reason: CORS header 'Access-Control-Allow-Origin' missing).
So nothing from Portal, our geodatabase or Map Services are being accessed when using Firefox. I also cannot see this being a huge problem...it almost sounds like there is one check-box or one configuration setting that was missed or has yet to be properly set.
Thanks again