Their are ways you can repair/replace the scroll wheel without replacing the Logic board. I did find a really good article, written by Jason Ball, that details how you can take apart the scroll wheel and hopefully repair it.
[link|https://jasonball.com/2004/09/09/how-to-disassemble-and-clean-your-ipods-mechanical-scroll-wheel-updated/|How to disassemble and clean your iPod’s mechanical scroll wheel]