Over the weekend, I learned how to move a website from one hosting account to another. I took these steps:
Website 1: I made a folder in my computer on the desktop. I went into Firefox FTP and copied the file out of the website into this folder. I then created a backup folder for My SQL database.
Hosting: I created a folder on the hosting account, where I wanted to move website one to. I then copied all the files from my desktop, in the folder that I created, to this new file in the larger hosting account.
*Note: I was to make sure I only copied the files inside the folder and did not move that actual folder inside the new folder on the hosting account. (I hope this is making sense)
Next, I created a new SQL database and loaded the backup file I saved on my desktop to this new SQL.
After that, I went into the WP-config file and copied my database information in there.
Finally, I went to the new hosting account, where I added the old website to it. When doing this, it asked me for the file it should point. I entered the exact name of the folder that I created with all the files I copied into it.
About an hour later, my old website was moved and working perfect in the new hosting account.
Go me! I have to credit to my boss for helping me out via text and GoDaddy support when I got a stuck a little. I understand how to do it now. Now, I have a large hosting account, so I will not have to do this again for a while.