If your computer is not coming online in Parsec, you might have an antivirus on your computer or on your home router blocking connections to Parsec's servers. The best way to figure this out is to press CTRL + SHIFT + I in the browser on ui.parsecgaming.com on your gaming PC and look at the console that pops up. If you see a lot of errors reporting something similar to:
Your anti-virus or firewall on your router is blocking connections to
wss://signal-load.parsec.tv, which is the system that manages whether or not your computer is online. This has been reported specifically with Arris Routers running Mcafee SHP. You can follow the instructions on this site and fix this by making an exception for parsec.tv.