Joe,
Glad you got it working.
The liveCD will not save anything to your computer. This is by design to prevent someone from accidentally damaging their Windows installation. If you would like to save the radio files, I recommend one of the following:
1) the "easier" method: after you boot the CD, insert a USB flash drive into a USB port. A window should open. At the top of the window you should see something like 'media disk' or 'media-4B3A' (just examples, not exactly what you will see). This is your USB drive. Linux doesn't use drive letters like Windows does. Anyway, in Chirp, use Save As and either save to the folder /media/whatever (from the top of the window) or save to the desktop and drag and drop. Note: do NOT pull the usb drive out until AFTER you shutdown/reboot the computer. Doing so could corrupt the files on the usb drive (Windows used to be like this too).
2) the preferred method: create a bootable USB (liveUSB) using the instructions on the wiki page of the download site. From there, boot to the USB drive. When you save, it will save to the USB drive. Same warning as above, don't remove the usb drive until after you shutdown/reboot into Windows.
Several people use the liveCD or liveUSB as their primary radio loader, but honestly, that isn't what I built it for. My intent was to get people up and running so they wouldn't throw the radio across the room. Then, knowing that the radio works, the user could get Chirp working on Windows at their leisure.
Let me know how you fare with the save.
Bob