I had two friends who had nonworking XBox360 consoles that were out of warranty. I refused to let them buy new ones until I knew they were beyond hope.
The first console did not spin the discs in the drive. It only needed some superglue on the spin motor because the factory glue had detached. Ten cent fix.
The second console had a bad laser motor in the drive so I went searching for a new one online. I had read that the drives were matched to the console but I thought if I swapped the circuit board over from the bad drive into the working one it would pass the handshake. Using the old board and new hardware it worked like a charm - nice try Microsoft. My friend had a working old console for $40 instead of a new one for $300.
If you are having problems with the CD drive on an XBox360 there are three motors that can be the problem. If the disc doesn't spin the holder on the spin motor may need to be re-glued or the motor might be bad. The eject motor and laser motor can also fail. However you may be able to find a replacement drive online if you search for "XBOX CD drive" with the same part number. If you find a match you can unplug the circuit board from the old one and swap it over to the new drive which will allow it to be recognized by the console. Motors can fail but the chips on the board should be fine. You lose this one Microsoft.