What SRG said. Personally, I would wrap a couple of towels around the desktop case, cushioning the corners, and strap it into a trolley bag. That would protect the laptop and provide a bit of cushioning incase your trolley bag hit someone inadvertently.

To be sure, BAA Security might question why you're taking a Desktop PC in your hand baggage, but their screening will show that it doesn't hide anything dodgy - does it?

Before you go, I would advise making sure there's no porn, soft or otherwise, on the hard drives (sometimes, in your internet history there may be "Adult Friend Finder" or similar adverts hidden away as well). It can land you in a lot of bother in less liberal parts of the world if customs decide to inspect your machine closely!