I've traded in 2 less than perfectly running PS2's to EB and GS respectively. The one I traded into EB was a 50001 model with a failing laser, which was cleaned at an indy shop just prior to me taking it there to swap for $100 in credit(with 2-3 games, old deal).
The other one, was a 30001R that I swapped away to GS. I kinda pitied those clerks who tested it, as I heard it scratching rings in their testing discs, but I didn't say a word.
I just grabbed my $60-65 in credit from them and split real quick. Thing is, I paid $30 for that one from an indy shop locally. So I essentially 'doubled' my money in a way.
I paid $100 a year earlier for the 50001 and played it ALOT in that year. So, I got more than my $$$$'s worth from it before I swapped it to them.
And I just traded in a 39001 about 2-3 months ago to EB, it was dead as a doornail. I took it apart down to base components and re assembled it like nothing. But, I still couldn't figure out how to fix the video problem it had.
So, off to EB it went. They took it in, no questions asked, just because I said it was 'dead' or broken.
So yeah Sephitor, you can just swap it into EB/GS and they SHOULD take it as is. But you'll only get maybe 25-30 in credit for it.