broken ps2 disk drive/reader thingy

So last july I broke my ps2, after two months later I was told that my ps2 disk reader thingy(the thing that reads the game disk) was broken.(you can probably guess that i got a new ps2) So my question is kind of two questions.
Do they sell ps2 disk readers online? offline?
and if I change the region of the disk reader is in would that mean I could play other region ps2 games?

Also I have a slim NTSC/UC ps2.

 

The "reader thinggy" you're talking about, is the lens. Either that, or the motor. To answer your question, replacement lenses and motors are sold online, but that means you would have to go under the hood in order to use it, which in turn would invalidate your warranty(but I take it, that it expired years ago).
As for changing the region, I don't know what you're talking about there. It is possible to play region-restricted DVDs(Action replay MAX allows you to do this), however you seek a modchip in order to play PS2 games from other regions.

Hope I helped.