Hello ParkviewJosh,
It sounds like there are 3 issues at play here, one your discs arent showing on the desktop when there is a disc in the drive. Your disc is stuck inside the drive, and your computer is not burning a disc successfully.
Lets start by getting that CD out of the drive with the following article:
Tip: Make sure the CD or DVD disc is not in use. Quit all applications that are using files on the disc.
- Press the Media Eject key at the top-right corner of the keyboard.
- If that doesn't work, drag the disc's icon to the Trash.
- If that doesn't work, restart the computer, then hold down the mouse button or trackpad button while the computer is starting up, until the disc is ejected.
To restart, choose Restart from the Apple menu.
If you are unable to remove the disc from the drive please contact Apple, contact an Apple Authorized Service Provider, or make an appointment with an Apple Retail Store for additional troubleshooting, evaluation, or service.
From: If you can't eject a CD or DVD or open the drive tray
http://support.apple.com/kb/ts2097
Once the CD is out, you can use this article to help troubleshoot why the disk may not be appearing on the desktop.
OS X Lion: If a CD or DVD doesn’t appear on the desktop
http://support.apple.com/kb/PH3997
And to help troubleshoot CD burning on the computer, try the steps outlined in the following article:
iTunes 11 for Mac: If you have trouble burning a disc
http://support.apple.com/kb/PH12149
Thank you for using Apple Support Communities.
Cheers,
Sterling