Hi,
while you have not deleted the laptop from the server, the files should still be in.
They are only accessible from another client PC by starting the console from the connector in the system tray.
If you cannot access the server from the other machine that way you may have a name resolution problem (If this is the case post the output of ipconfig /all entered in a command prompt on the client and the server.)
Does that machine have the Connector software installed and is regulary backed up on your home server?
You also can attach the disk of the failed laptop (or another empty disk in at least the same size) to the failed or another PC and try to restore the backed up volume to that disk using the most current
WHS Client Restore CD.
Best greetings from Germany
Olaf