You'll have a hard time finding people that are willing to try Linux.
IMO, if you REALLY wanted to differentiate yourself as a computer company, you'd have to do something really unique. Something like uncommon (Windy?) or custom-built cases, custom sleeving on all cables, etc. It could be very cost and time prohibitive.
The biggest thing to keep in mind is that the more custom work you do, the higher your price is going to be. The higher the price is, the more reluctant people are going to be to line up as a first-time buyer from your company.
If you're serious about doing this (and I applaud you, I've toyed with the idea in the past myself), your best bet may be to see if you can team up with some kind of OEM that makes specific parts, and see if you can work out a deal to build computers using their products exclusively. Something like Corsair (Case + PSU + memory + heatsink) or Antec (case + PSU + heatsink).