After spending the morning working on this, I finally figured out the problems and most importantly, how to get subsonic back up and running! In case anyone else encounters this issue, here is what I found out and did to get things up and running again...
First, after digging up some older posts listed elsewhere, I realized that the username and password credentials are computer specific. Meaning, when you set up subsonic, the username and password are stored in your subsonic/db folder rather than somewhere on the internet or network like I originally thought. That being the case, if you simply install subsonic on a new computer (as I did), and then enter your username and password, that won't work. What you need to do is copy the subsonic/db folder from your old computer (or the one that originally had subsonic on it working) and overwrite the subsonic/db folder on your new computer. Once I did that, I was able to gain access just fine. If you no longer have access to your old computer, I believe there is still a way to modify the script which would solve the issue - however, you will need to ask someone else on how to do that. Back to my issue...
I thought I was finally in the clear but soon discovered that I still could not access my music over the internet. I used the site
http://www.canyouseeme.org to see if my port (8080) was being blocked. I found out that it was. Therefore, I realized that I had to make some changes in my port forwarding settings most likely, although had no idea what do at that point. Being that I am not very proficient in the area of networking (as this post can probably scream), I "dumbed" around a bit in my router settings and found the solution. I located the port forwarding rule that I set up with my old computer. What I didn't realize at the time (again, obviously showing my ignorance) is that the new computer had its own IP. Therefore, within the port forwarding rule that was already set up, I just simply changed the IP that was listed to my new computer's IP. After doing that, I checked
http://www.canyouseeme.org again, and this time, it was able to "see" port 8080.
Now I thought I was definitely good to go, although I quickly found out that wasn't the case. Long story short, I didn't have the correct settings listed in the subsonic control panel like what I had set up on my old computer. Once I changed the port number to 8080 (from 80), I was finally in the clear. Therefore, make sure you have the proper settings in the control panel or you will continue to have issues as I did until the correction was made.
To test, I went to my laptop and tethered it to my cell phone (thus getting off my home network). Well... I was able to access my music without any further problems! Delighted I am as I LOVE subsonic and use it all the time. I have already donated 20 bucks, but after not having subsonic working the past two weeks, I will donate another 10 bucks or so because of its value and the appreciation I have for those that created it!