For some reason, when I click on the application shortcut, nothing is happening
Can you get to a Command Line prompt and run it by name? OrionNetPerfMon.exe
Are your Solarwinds services which are set to AUTOMATIC showing as STATUS 'started'?
one other point of interest.
sometimes the profile in Windows will not display/link (nor execute) a shortcut due to the login id. do you think this could be your case?