So it can have its own network. I see it as an available network I can connect to on my computer. So is it already independent of the router?
So it can have its own network. I see it as an available network I can connect to on my computer. So is it already independent of the router?It can't be independent of the cablemodem (unless you're "stealing" Internet connectivity from a neighber). If you have a stand-alone router, then you may have the choice of connecting the Roku directly to the cablemodem or to the router (which is connected to the cablemodem).
For example, I have a "private" router, with WiFi, which I use for my home networking. This keeps my network separate from the cable company's network. My "private" router connects to my cablemodem, which is treated as an untrusted, outside network. Because the Roku has no need to access my local network, I plugged it directly into the cablemodem, where it can access the Internet (as it needs to do), but it can't access my computers (which it doesn't need to do).
But, most people don't bother with anything that elaborate. They just use the WiFi hot-spot provided by the cablemodem, and everything works.
Getting back to your original problem, if you haven't done so already, please reset the networking on your Roku. It only takes a minute, and it might fix whatever problem you're experiencing. Just be aware that if you are using the Roku's WiFi connection, then you will need to enter the SID (name) and password of the WiFi hotspot you are using.
Sorry to be so wordy. Please feel free to ask further questions if I'm not making myself clear.