Some fixes are easy, including the stuck disc. It can happen for a variety of reasons that we won't go into here. After all, when the Titanic is sinking, you don't stop to yell at the iceberg. So let's just eject the disc.
The fix is simple. After trying the obvious (hit the eject key, drag the disc into the trash), restart the machine and as it starts up, hold down the mouse button (or trackpad button if the offending Mac is a laptop). The disc should now eject as the Mac continues to start up. If not, you may have optical drive issues to worry about. But chances are you'll get mom's extended edition Murder, She Wrote DVD ejected safe and sound.