First try a uninstall of the cd drive from device manager then reboot and let windows reinstall.May be worth going into the safe mode and see if you have the same problem/reaction from the drive.
(also)Of the cuff suggestion.
"If" drive it's fairly old? you could try holding in the tray with light pressure after inserting the cd.(it did work for me,but dont ask me "Why" :)
Not saying it will cure the problem for sure.Had simlar problems way back with ejecting, mind you ) that was due to my knee cap hitting the disk holder and knocking the tray of the rails.Expensive mistake in those days.