I'm using this router bought from Amazon a year ago.
https://www.amazon.co.uk/dp/B0031SUB4S/?tag=b3d-21
Ok, so you shouldn't be having any NAT issues. You could try loging into that modem and assigning your PS4 to the DMZ. It will basically bypass the firewall for your PS4. You'll have to give your PS4 a static ip address. If everything works well, then you know it's probably some issue with the firewall, port forwarding, UPnP. If you put the PS4 on the DMZ and you still have issues, I'd say there's a good chance it's a line issue or an isp issue.
Also, upgrade the firmware if you haven't. Good practice for security anyway.