I know this is old but I wanted to give more of a complete answer.
1st check if the laser moves when the lid closes or first powered on. If it don't move then most likely it is the two switches that detect when the lid is closed. The one in the back side of the system near the middle is common to have issues, soldering a wire from one side to the other will work well and I have done it several times.
2nd we should beable to rule out the switches so now the question is, has the system been worked on before. If it has, the ribbon cable for the motor that spins the disk is common to get messed up where it plugs in.
3rd If everything appears to be working correctly but the disk won't spin, try a CD in it. It is very common that the cause is that the system don't "see" a disk in the drive and most common media is DVD so that is what wears out. If it reads the CD fine, then most likely it is the laser.
4th Just to note as above, there is a small break for the disks and if that is not released when the lid is shut, it will have problems reading the disk, but it WILL spin still.
5th Once I had a "worm" motor go bad that moves the laser. The case I had it would see the disk but would not read it. Found the laser didn't move at all. When the system is turned on or the lid is shut, the laser should always move to the center of the disk and a small switch is pressed so the system knows where the laser is at. Also the switch can go bad and continually try to move to laser to the center causing a clicking notice that don't go away until you shut it off.
Hopefully this can help answer some questions for the readers of this question and point them in the correct direction.
Source: Fixed and modded PS2s for over 5 years