I'll give you the same advice I've been giving people for two years.
Remove all labels from the underside of the laptop (I assume you're talking about a laptop, if a desktop the stickers that are on the laptop are on the rear of the PC.).
After that's been done, remove the HD (Either for analysis (Might get some CC's or other 'interesting' things.

or to format.).
Then place a new HD in the PC and disable the Wi-Fi card, using a USB Wi-Fi dongle in place of the Wi-Fi card.
XxXxX
An idea I came up with a while ago for securing items which can connect to the net via Wi-Fi would be to purchase a domain, stick a Google search bar on the front page, as well as links to sites you often visit.
The front page would be the default for all devices you owned.
Said hompage would be fitted with a means of viewing the IP's that visited it as well.
Which means when a device is stolen from you, using the Wi-Fi on the device will reveal the thief's IP address. The IP address can then be used to track down the thief.
I came up with the idea after my friend had his PSP and iPod Touch lifted from his jacket in a lab. Between the two of us we were convinced the thief was someone in the room and lifted the devices after they heard my friend talking about using the Wi-Fi on the touch.