With the power off, connect the laptop drive to either the adapter or directly to the motherboard of the new desktop. If using the adapter, turn on the power before powering up the computer.
Once inside windows open Windows Explorer and copy your files from the laptop drive (might be drive E: if you have a CD/DVD drive) to the C: drive of the new desktop. You might want to create a new folder called LAPTOP and put all the files in there to complet the process, and shut down the desktop. Now you can disconnect the laptop drive and put it back in the laptop.
Power up the desktop and organize them however you feel. Power up the laptop and delete them.