I'm no expert, far from it. And (as you can see on the forum) I'm having my own wifi issues. With those caveats, though, I can offer these few ideas.
A) concentrate on wired connection first, there are fewer issues to worry about and you'll be able to update Synaptic, download patches, do whatever to solve the wifi issues after that.
2) Go to the "Configure Your Computer" icon, the PCLOS circle with wrench and screwdriver. Find the Network & Internet department. Upper right: Set up a new interface. Clicke Wired (Ethernet) and follow the prompts to set up a "new" connection. You can then delete any non-working "connections". And don't forget to call your new connection "Atari" like I did, this will solve everything. (That was a joke.) You might even want to create a new user account to do this - that way you know everything is at default values. Maybe??
Lastly) run "lspci" and "lsusb" commands in a terminal and post the results. These are requested by people who know. I cannot interpret them, but they are requested by the folks around here when trying to solve connection issues.
(P.S. I read somewhere around here that when you get to Synaptic you must first click Reload then click Mark All Upgrades then Apply anything Synaptic found. This sets up Synaptic properly to go forth finding the stuph you really want.)