I was unfortunate enough to have bought one of the early-model PS2s
(model 39001) with the infamously faulty disc drives.  6 months ago,
after many problems, the drive stopped reading discs altogether. I
then paid $107 to have some sleazy repairman "re-align the laser". 
Now it's acting up again and I don't want to pay another $107.  Is
there anything I can do?  How do you open these things up? Can I
repair it myself?

Sony realized their error, discontinued the old model and started
selling model # 50001 (with a good disc drive).  What do they expect
people in my position to do?

After it broke the first time, I would have just bought a new one...
Sony tends to have very, very faulty products. There are hundreds of
documented problems witht he PS2, and what's funny is there is already
a list of problems with the soon-to-be released PSP.

I would be very surprised if the guy re-aligned the laser. Lots of
reasons which I won?t bore you with. What he most likely did, and
vastly overcharged you for the privilege, is clean the (final) laser
lens. It effects a miraculous cure and kids say a cursory ?thanks?.
Hero for a second.

So long ago I can?t remember if you have to take it to bits a bit to
do it, but all you need to do once the lens is visible is check with
an eyeglass if the surface is ?bloomed?. If so, *very* gently clean
with a damp, slightly soapy, tissue tip. Hold it in tweezers. Finally
dry with another tissue tip. Don?t touch the tissue tip because grease
comes off even clean fingers.

You should be left with a shiny blue lens. Don?t use alcohol because
it can damage the blue coating. You?ll notice the lens moves as you
clean it -- it?s supposed to. Very fragile but you?ve nothing to lose.
Incidentally, check first that it?s not just fluff etc on the lens.

Best