My brother-in-law's computer appears to be infected, can't get browser to stay up, task manager and run also won't stay up, etc. It looks like HiJackThis may be a good place to start but he can't even get it downloaded. My question is can I download it and then make a copy to install on his computer?
You don't have to "install" it. Just make a folder for it, and copy it onto his hard drive.
Important: Create a folder on the C: drive called C:\HJT.
You can do this by going to My Computer (Windows key+e) then double click on C: then right click and select New then Folder and name it HJT.
Copy HijackThis into this folder.