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Easiest way is to open the case on your computer (WITH THE COMPUTER UNPLUGGED!), undo the screws holding your CD drive in and remove it. You may well find that the only thing stopping your CD door is a piece of the broken CD caught between the door and the case.
Replace the CD Rom and put the CD power plug and Motherboard / soundcard plugs back on & turn on the machine to see if it will boot up and close the CD door.
If it does not, you may well have to replace your CD-Drive or a least get it serviced. If it does all is well. Turn off the computer again, replace the screws holding the CD-Drive in place and put the cover back on before restarting.