you live with him, take the laptop back, and beat the living piss out of him,throw every last damn thing of his out the window and put a free sign on the lawn while he lays there crippled.

If you have online banking there's a chance that the online statement will have that name of the store you bought the laptop from as well as the corresponding price

Still you can get your laptop back if it was running Mac or Windows, cause the first time you create your it asks for mail ID. It registers your device under your mail ID, so can show it under your devices in your account.

You can show the receipt if it has the last 4 digits of your card (assuming you paid with a card) and then show them the card to show it matches. They can't let someone get away with stealing someone else's personal property without as much as investigating. They can't go by word of mouth, they need physical evidence.

I'm thinking it should be fairly easy to prove it was yours. I'm assuming you didn't pay cash for it so there's a paper trail.