Your laptop has a Intel WM3945ABG wireless card (same as in my ThinkPad R60)
that is supported by the iwl3945 kernel module, and it's blacklisted in
Linux-libre because it relies on a proprietary firmware blob.
This is an older generation model, and it's 2x longer that your Foxconn card.
It will find and should work, but you would not be able to securely mount it
with screws, so it will not hold in place. You need to buy a special metal
strip, that you can attach to the card (look for it on eBay, or your local
auction site).
The adapter is located on the opposite side of the mainboard. Here is a
picture what it should look like:
https://www.nt-computerservices.com/images/sony_vaio_PCG-7N1M_wireless%20card.jpg
Can you make a photo of the bottom of the laptop?
