We'll show you how to export the Self-Signed Certificate from the original box onto a new box.
Go onto the original box and open a command prompt, and type in 'mmc'. Hit enter
In the MMC applet, add the Certificates snap-in. In the wizard, choose Computer Account and Local Computer.
The certificate that we want should be under 'Personal'. Find the certificate and right-click, choose All Tasks > Export
Fair warning: we're not security experts, we're developers just trying to get the job done. There are lots of smart security people out there that understand 'private keys' better than we do. OK, the kid that asked you if 'you want fries with that?' yesterday has the same level of understanding as we do.
We're going to choose the route that seems less complicated and choose not to export the private key.
Same warning here. We'll choose the DER encoded binary option.
Save the exported certificate to a network share, because we'll want to access it from the other machine.
Now open the Certificate snap-in on the new machine, using the same procedure outlined above.
This time find the Trusted Root Certification Authority, right-click, and import.
That should do it.