Hello Susan,
It could very well be the result of a damaged CD-ROM drive.
One more thing I would do to rule out a defective drive:
Try inserting the factory original DVD restore disks. These are bootable, and can be used to start up the computer.
First, I would try inserting them with the computer already booted, sitting at the main screen. Then, see if they are automatically ejected.
If they work, then you know it is some strange glitch.
If they are ejected, then try booting the computer from them, by doing the following:
Turn off the computer
Insert the restore disk labeled "Disk 1" as far as it will go without much pressure. This will leave half the disk sitting outside the computer. It should just be resting there.
Turn on the computer
Immediately press and hold the letter "C" on the keyboard.
Then, immediately try to insert the restore disk. If the drive resists, don't force it. Wait a few seconds and try again. Keep holding down the letter "C" while you try.
Once the disk has been inserted, keep holding down the letter "C" until the computer shows the familiar "Mac OS" box with the blue progress bar.
Then release the letter C, and let the computer finish booting up.
By holding down the letter "C" at startup, you are telling the computer that you only want to boot from a CD or DVD. If no disk is present, it will usually keep looking for one as long as you are holding down the key. That's why I suggest holding the key down as long as it takes to get the drive to accept the CD. Sometimes the drive will not accept the CD immediately, it needs a few seconds to become ready.
Anyway, if the computer boots from the CD-ROM drive, then I would suspect the drive is fine and you have some other problem with your software installation. This might warrant re-installing your OS from the CD (using the same steps mentioned above to boot, but then do a restore from the disk).
Alternatively, if you determine that a re-install is needed, you might just download and install the latest OS X 10.4.3 "Combo" update. This may replace enough of the system files to correct whatever your problem is. Be sure to get the "Combo" update as it contains the most complete copy of the OS.
If you are running OS 10.3.x, then I would download the 10.3.9 "Combo" update instead.
The advantage of re-installing the updates is that they restore a good number of your system files to "clean" versions without requiring you to re-install everything on your computer. This would minimize the risk of losing data (especially since you cannot save anything to CD at the moment).
Let me know how this goes.