After disassembling the drive, I realized that the optical drive had a
black plastic cover that sorounds the laser diode (or laser light
source, whatever that is), and it was broken and I in fact found that
broken piece. I then glued it back. ... but well 
... it cant read CDs
anymore.
Let's see if I've got this right.
The plastic cover with an opening for the objective lens was forcefully torn
off and now the drive won't work.
It may very well be possible that, with the forced opening that sheared off the
shroud, damage may have also been inflicted on the objective lens, lens focus
voicecoil drivers, and the lens suspension.
If this is the case, the pickup is totalled.
I wonder if its already hopeless to make this CD drive work (I
can of course buy a new one, but IŽd also love to learn and experiment
with the mechanism of this one.
You can't really repair the pickup and expect it to be reliable again. You
will have to replace the pickup if parts are available for sale and if it's not
too expensive.
It is much more economically feasible to replace the drive rather than attempt
this kind of repair.
At least cheaper CD-RW drives can be very decent. Lite-On makes fantastic
CD-RW drives and they don't cost an arm and a leg. - Reinhart