I did it the old fashioned way and after finding out which screws need to come out its very easy.
The PS2 is pretty much 2 rectangles stuck together: a bigger and smaller one. Turn it over and remove the screws from the bigger rectangle to take off the top. Now just focus on the small screws on the DVD-ROM. Take the DVD cover off, get a moist Q-tip wipe the dust off, then dry with the other side. Should work just like new now.