You'd think he'd want to find out more about Woody and to get more toys from the old show, but then there wouldn't be any character introductions in Toy story 3.
I think you mean Toy Story 2. Also I assumed Woody was a hand me down from his Dad. This is hinted at in the 2nd movie since Woody's show is in Black and White which wouldn't have been used at the time the movie takes place.