Hi!
Could be many things.
It's possible that the laser died and is even unable to see the disc, hence it won't move.
It's also possible that the worm motor is broken causing the laser not to move.
And it could be the laser's clamp/bracket.
I always check the laser clamp/bracket first, if it's fine, I replace the laser. Still not working? Then I solder a new worm motor in.
You can check this guide: Nintendo Wii DVD 드라이브 렌즈 교체
Both are easy to replace (worm motor is a little soldering experience required).
I'm afraid you need to spend some money here. Glady, a laser and a worm motor is not that expensive. I would start with a new laser first, they are known to fail.
If you don't want to refurbish the drive, then just replace the whole drive and this should do the job as well. But this will be more expensive