Streaming network issues - need a geek

What model is the router? If relatively new, you may have customer service available from Netgear for free. Their paid service, I'd be hesitant about. The one time I tried it, it cost me to have them tell me to reset everything back to default (which didn't help).

Because network addresses are assigned by the router, you’ll never be able to run a cable directly from the modem and use the router at the same time, as you noted. Also, the router provides Network Address Translation, which is a safety measure you’d best not do without.

It would be unusual for a router to restrict speeds unless specifically configured for that. Cables could be a problem. I’d suggest using decent cables -- not "audiophile" Ethernet cables -- that are Cat 5e, Cat 6, or Cat 7. Try swapping cables, as they do fail from time to time

After making changes, sometimes it helps to shut off modem and router and let them boot up again.

That’s about all I know. There is a Small Net Builder’s forum available online where you can get more free advice. Like the free advice anywhere (including mine), it might be good, bad, or indifferent.

I misread the original post -- now I see that you are connecting the streamer by WiFi.

Yes, as others have said, the modem needs to be in pass-through (modem only) mode. That means its WiFi will be off. I believe most Netgear stuff has a sticker on the bottom with its default IP address, user name, and password. You can contact the modem then from a Web browser on your network and check & change settings.

If you can run a cable from the streamer to the modem, why not run the cable from the streamer to the router instead? Most of them have 4-8 Ethernet ports in the back. (I just checked; yours has four.) If not enough ports, a $20 unmanaged switch will help.

Routers I’ve used consider wired and WiFi devices all to be on the same network by default. They draw IP addresses from a common pool. What I’m trying to say is, they can talk to one another.

(BTW, Category 8 cable is absolutely unnecessary at those speeds. Cat 5e is plenty, though there is nothing wrong with Cat 6 or Cat 7. My understanding is that Cat 8 is shielded and the shield grounding is said to reduce isolation between devices. Some very tweaky folks complain of higher noise floor, but I have no experience with that.)

+1 @jgoldrick 

Yes, add a switch -- or more than one switch -- NOT a second router. The kind of switch you need is something like this:

https://smile.amazon.com/Ethernet-Splitter-Optimization-Unmanaged-TL-SG105/dp/B00A128S24/

You can think of it as an "extension cord" for Ethernet.

You can't run devices from both the modem and the router because you are then creating two separate networks that don't "know" how to talk to one another. This can cause all kinds of problems.

To put it another way, the router runs a DHCP server -- it assigns network addresses to your devices. It is not advisable for the general home user to run two separate networks, as it can cause the problems noted. That's why the modem must be in passthrough mode and one device (the router) assigns the addresses and connects devices.