So it's already connected but only showing black screen, correct?
If yes, then network connection is not the problem now.
For further analysis, could you please download the spacedesk diagnostic script here, then extract it.
Inside you will find spacedeskDiagnosticTool.cmd, just right-click it then run as administrator.
This script will start a debug view app to capture spacedesk debug traces.
On step 5 it will prompt you to reproduce the issue (by connecting the viewer app and wait for the black screen issue to happen), make sure to do this before pressing any key to continue.
After the script is done, a folder will be created on the same folder as the script file which contains various log files that we need for analysis.
Please right-click it -> Send to -> Compressed (zipped) folder, then attach the *.zip file on your next reply.