It's not a serial number the installer is looking for, but the Apple ID user name and password you created for the App Store. Knowing the Mac's serial number won't help at all.
The serial number also has nothing to do with logging into the user account. You need to know the account password, which would be whatever password you used.
Thank you for your response. I was aware of this and tried to install OS X using the recovery by entering my icloud account, but kept getting the error about the account not having purchased the OS (It turns out I had to wait about 20 hours before receiving the actual OS X License). It looks like it didn't work because I purchased OS X through the App Store website, instead of the "preferred" AppStore mac app.
I recently received the confirmation from "Apple Volume Licensing", and will add it to my purchases through iTunes.
I wanted the iMac serial number to contact customer support through the Support section of this website... But that issue is now obsolete as I have installed OS X from a USB drive I got my hands on from a friend who had already purchased OS X Mountain Lion.
I ended up contacting Customer Support by phone and was told it could take up to 48 hours for my order to be processed.