Where can I find the original GID to reconnect a freshly installed PRTG probe to its server after a hard drive failure? Is it stored on the server? 

The GID of a Probe is stored in the configuration file "PRTG Configuration.dat" on the PRTG Core Server (see How and where does PRTG store its data?). You can open this XML-File with any editor and then simply search for the exact name of the probe, without the content from the brackets "(... Probe on ...)". Please see the following example:

                <name>
                  Local probe
                </name>
                <ownerid>
                  100
                </ownerid>
                <position>
                  10
                </position>
                <priority>
                  3
                </priority>
                <probegid>
                  {E014D5DB-08D9-49BC-8298-AF37EA363F8A}

The property is named probegid in the XML of the configuration file. If the Probe is deleted though, you may need to look into an Automatic Backup of the configuration file.



Disclaimer:
The information in the Paessler Knowledge Base comes without warranty of any kind. Use at your own risk. Before applying any instructions please exercise proper system administrator housekeeping. You must make sure that a proper backup of all your data is available.