What do you mean with "copper band"? The 8 circuit flat flexible cable? Yes it's essential and must be replaced if broken.
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In the "corner of the track pad", there's an adhesive metal fabric band connecting a ground pad with the frame metallization. It has been apparently replaced by a different ground connection method in the new device and won't be needed any more.
Purpose of the ground connection is most likely only EMI suppression, not related to mouse pad function.
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If the mouse pad doesn't work, I would expect either some electrical/functional incompatibility or a broken flexible cable.
By the way, are you sure that the old mouse was actually defective?
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If the mouse pad doesn't work, I would expect either some electrical/functional incompatibility or a broken flexible cable.
By the way, are you sure that the old mouse pad was actually defective?