Assuming your new desktop isn't a NUC or something, chances are the only thing you'd be able to pull out of a laptop is the HDD or SSD, though that isn't guaranteed. Laptops usually use 2.5" HDD's or SSD's, but sometimes they use 1.8" versions, or mSATA or M.2 type drives, which may or may not be compatible with your new desktop.
The wireless card is more than likely integrated into the motherboard of your laptop. Chances are there is nothing worth salvaging out of it for a new desktop— as even the hard drive (or whatever you have) is not likely to be useful, even if it is compatible, since an old laptop HDD is probably no larger than 500GB (probably less than that) and pretty slow.