Sue,
If you have not successfully completed the burn, you're not losing a "burn count". It doesn't count against the 7 burns. And it's not 7 burns per song, it's 7 burns per playlist, which means if you reshuffle the songs into a different order or add or remove a song to change the playlist, it's a new playlist and you get 7 more burns.
For future reference,
the support page for your computer is here. And there's a note that there's a critical BIOS update, but I don't that's your problem and I don't see anything there to help you.
You do have old firmware on that LG CD-RW 8080B, which I assume is what you're trying to burn with. To get the new firmware from the LG site:
Go to
http://us.lge.com/www/support/index.jsp
Click on "Driver Downloads"
Click on "CD-ROM(Writer)"
And if you go to the third page (that's those little numbers in the bottom middle of the page), you'll see an entry for the CED-8080B.
Click on that and you'll get the page with the instructions for upgrading firmware and the link to the file to download.
The latest version of the firmware is 1.06 and you have 1.03.