Sam_missles :
No. Laptop HDDs have different ports. If you just want the files you could do a file transfer to a full-size HDD.
Half right and half wrong.
Laptop(2.5 inch) IDE drives have different ports that combine power and data.
SATA 2.5 inch drives had the same ports as a desktop one. They only use 5 volts, but still retain the same ports.
2.5inch SSDs(same form factor as 2.5 inch sata hard drives) are the same for most desktop and laptops(while some can be thinner and come with a spacer to make them thicker.)
Notebook optical drives to have different plugs(SATA drives use a condensed plug combining 5 volts and DATA), but adapters are available to fix this issue.
smaller and thinner laptop drives use a smaller plug to save space. msata and other various card type ssd's are different and require adapters if your board does not have a slot for them.
I use 2 x 2.5 inch drives and one 3.5 inch drive in my media center as well as a notebook optical drive(with the adapter needed for that part). No issues at all. My computer for gaming has 2 x 2.5 inch ssds and a notebook(slim slot load) optical drive as well.
Using an old drive is fine, just remember to remove the old operating system data so your system does not try to boot off of it.
I recommend you first get your notebook drive working then copy files the current drive. Erase the notebook drive and copy data back to it. At this point you can clean install Windows if you wish to on the desktop drive. Disconnect the laptop drive when installing a new OS just to make sure it is not touched.
If you lack space on the desktop drive for your files, you may have to play musical partitions on the notebook drive to move files to another partition and remove the windows partition then merge them after. This takes 3rd party software most times and you have to take care to not do anything wrong.