The garbage convenience center has an electronics recycling area. I just bought a brand new laptop for $170, so unless you have like an 1-2 year old laptop that cost you $1000+ originally, I highly doubt there is much of a market for it. Not many laptop parts are interchangeable, so the parts inside are not worth much any more.
I remove the hard drives before I dispose of our old computers. I transfer the data to a 3 TB drive. Then, those hard drives get to meet Mr Magnet, Mr Hammer, and then Mr Saw before I dispose of them.