I have a few ideas for you.
First, turn off the computer, unplug the Lite-On's IDE cable (but leave the power cable in the drive), and then turn the computer back on again. See if the red light comes on abnormally then. If it doesn't, you know that the drive's probably OK.
If that doesn't work, reconnect the IDE cable to the Lite-On (again, with the computer off) and try upgrading the firmware.
Although I don't know for sure, I think the LTR-52246S should be able to copy anything that the LTR-32123S can copy. I think the warranty is only one year, so you probably won't be able to get a new drive if your old one is broken.