I think the little spin is a normal thing during power on.
Here is a breakdown of what happens after you hit the Start button to being a cd:
1: Lid switch is checked - if bad, you'll immediately get a warning to close the lid
2: System checks for closed limit switch signaling that laser is at innermost point
3: If switch is not closed, reset laser to innermost point
4: When switch closes, activate laser and check for CD. Lens will move up and down.
5: If disc is detected, bring disc to speed and read directory
The verbose version of this is detailed here:
http://www.repairfaq.org/REPAIR/F_cdfaq5.html#CDFAQ_005
It sounds like you're getting stuck at 3 / 4. You can use most digital cameras to verify if the laser is activating (newer iPhones and DSLRs probably not). If you have laser and no focus, the servo mechanism is shot. If you have neither then the limit switch is probably not being tripped.
Did I mention that these things are a royal PITA to service?