am new to this board recycling, am used to bulk shred metal recycling, and for the most part my scrap yard gives me some meager reimbursement for circuit boards... yesterday, I made an arrangement to recycle computer parts from a local repair shop... some of the boards are damaged or distressed, as the shop does not take the time to carefully dismantle their basket cases. do those boards just become e-scrap or if I identify a (let's say) a mother board, would it classify as a mother board despite being damaged or missing some parts?

It will always depend on how damaged.
A motherboard board split in half but having both pieces is still a motherboard.

A board with a bunch of missing ICs (chips) is going to be downgraded.

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