Normally you only choose the cable provider/internet provider when you are trying to setup a subscription that requires cable or satellite provider in order to use a subscription service on your Roku device.
You do not need to perform this step in the "setup" of the Roku device. Roku does not care who your internet provider is. Roku merely performs a check to see if internet access is present. (We may be able to get your cable to play through the Roku device later, but currently just need to get Roku setup first - two different setups).
From the above, looks like you may just be having a little confusion in the above during the initial setup of your Roku device. However, Roku asking you for Home or Hotel/Dorm is meaning Roku is having a little difficulty with your setup. The fact that the router is so far away could be playing into the equation but lets do something simple before doing a Factory Reset and trying again or using a mobile hotspot to setup the Roku device.
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Restart both your Roku device and your Router. When the Roku reboots, go to Settings/System/Advanced System Settings/Network Connection Reset/Reset Connection
Your Roku will once again reboot automatically. When the Roku boots back up, go to Settings/Network/Setup Connection/Wireless and enter your Wifi credentials. (These are the ones that you use to connect any computer or device to your network). Do not use your cable credentials unless they are the same. Use the wifi credentials.
Once it performs the network test (like it did before), see if you can launch the Roku Channel (probably installed already on the Home Screen).
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If the above does not work, post back and will try an alternate way to setup network. Make a note of any error messages you see on screen (should be some numbers and a message).
Just as a potential option, do you have a mobile hotspot available to you (on phone perhaps)?
Here's what I would do given your circumstances:
Take the "problem" Roku to the other set where your first Roku set up without a hitch. Swap the "problem" Roku in place of the "good" Roku and see if it will complete the setup. If it does, then take it back to its original location and see if it continues to work after being set up.