you can always try the trial of parallels for 30 days to see if it works, and if it does, problem solved ... but either way, you will need a Windows XP sp2/sp3 or Vista installation disk
and btw, there rly is no way we could know if your computer downstairs came with an installation disk
... just watch out for your serial, downloaded versions usually require an activation and that can be done only once! so the best way to go is if you have a retail version
don't want to get into illegal stuff here
edit:
I doubt you'll be able to play Warhammer 40k in Parallels though ... or do you mean some other version?? the table game you can definitely run, of course the laptop probably isn't a big enough board