Boot up hangs up.

[jerrybob]

Can a CD get stuck inside and the computer still accept another disk and work fine with the second disk?

 

[spinnerlys]

Mac doesn't boot
Force Eject a Stuck CD or DVD


Or reinstall the OS.

 

[fluffyx]

Can a CD get stuck inside and the computer still accept another disk and work fine with the second disk?

To answer your question, absolutely not.

If the steps that spinnerlys suggested in http://guides.macrumors.com/Force_Eject_a_Stuck_CD_or_DVD don't help, you need a new CD/DVD drive.

Many Mac service providers offer that repair at reasonable prices.