AE has problems working on the old PS2 model?
 

The only lightly scratched AE I bought refuses to work on my PS2 which is the older stand up type while it works fine on my brothers newer type the small flat ones.

I'm planning on getting the disc cleaned at a game store to see if that helps. I really don't feel like having to wait another two weeks for a new one not including having to send the old one back to the seller and getting a refund. Too damn much of a hassle for something that should be working in the first place.

Is this a common problem? Is AE known for not working on the PS2 or what?

Wait another two weeks? What about Steam?

It takes forever for people to ship crap and it takes even longer for it to get here.

I'm buying the playstation version of the game because I've always wanted to play it on there after playing the PC version my whole life (Which no longer works)

I have an early type ps2, my copy of AE works perfectly fine on it, especially considering it was the first game I ever had for the PS so is old and scratchy. It must be a problem on your end, only problems I've had on the PS2 were results from the more populous scratched areas. Mine isn't standing on its side though.
(Dare I mention what is so poisonous about the PS version so much that they always point to the PC version? PS version of the game works just as fine)

I once took a copy of Geometry Wars Wii to GameStation and they cleaned the disc for me in special machine which takes 1-2 mins. Needless to say, it works perfectly now.

OR you could rip the psx disc on your PC, burn it to a CD and run it using a PS2 softmod or SwapMagic.