I just got an old xbox from my friend and the disc drive doesn't work.

Is there anything I can do with it without replacing the disc drive?
And where would I even find a replacement?
(I have tried looking, but my Googling skills must suck since it only ever shows me 360 ones)

 

In google insert -"insert word here" if you don't want that word in the results

 

I believe the xbox drive was tied to the console like the 360, however as everybody went other modding ways it was easier to ignore and replacement/repair is tricky (most would instead head down the laser replacement path, give or take what I mention in a moment).
I will say though that a lot of the time the drive was not dead but the little rubber band inside it getting messed up. If the drive does not open then it might well be this. Take it out and clean it and the thing it runs on, possibly replace it if you can find something suitable.
Equally even if it does not eject normally then keep trying and it might eventually pop out. Stick a copy of splinter cell in there and do the softmod, after that ignore the DVD as it is of limited use.

You can do a hotswap mod, and yeah if it is an older one you could TSOP mod it as well. The ones that did not involve opening it up though did involve having a game boot.

 

Actually yeah, I was misremembering that list of mistakes MS made in the xbox thing, or a similar discussion.