If you can hear the sound of the CD rotating then it probably isn't the physical connection.
Once you get it opened as suggested by dandelionweeds then take an ear bud and dip it in some aftershave or perfume and clean the lens (that round clear plastic thing) as shown in the pic. This usually fixes it... just make sure you let the lens dry for about 2-5 mins and don't use too much pressure.
If you are trying to read writable CD's and have a CD player (not DVD) then you will have to check if your CD player can read the +R or -R cd's ... some players cannot read both. Same applied for DVD+R and DVD-R.