Can I change Apple TV settings from a laptop?

My best advice, in my opinion, is to recommend you purchase a replacement remote, however, if you are averse to this suggestion there are some workarounds which may apply in some situations.

Depending on which Apple TV you have you may be able to set up the Apple TV from your mobile device. You will need a 3rd generation Apple TV for later running software version 6.0 or later and an iOS device running iOS 9.1 or later.

Restore your Apple TV. When the Apple TV setup screen appears, unlock your iOS device and make sure Bluetooth and Wi-Fi are turned on. Touch your iOS device to Apple TV and follow the onscreen instructions on your iOS device and Apple TV.

Automatic setup doesn’t transfer account information for third-party apps such as Netflix or Hulu and doesn’t turn on iTunes Match or Home Sharing.

If this doesn't work, you don't have an iOS mobile device or your equipment doesn't meet the minimum requirements, you may wish to look at ciderTV for Mac OSX, once you have installed the app on your Mac...

1. Check that Bluetooth is On & Discoverable;
2. Keep Bluetooth preferences window open during pairing;
3. Connect Apple TV to your Mac via USB cable and reset it in iTunes app;
4. Turn Apple TV on and wait until it finds your Mac. A pop-up window will appear that says “Pairing Request from Apple TV”;
5. Tap "Pair";
6. You will see CiderTV control interface with buttons.

Hi SquareSpoon. Are you sure your dead silver remote doesn't just need a new battery?

If it's really broken, you can easily order a replacement from the Apple on-line store. And you will need it eventually, to set up a new WiFi, unless you get Cider TV working.

(I didn't think the appleTV had a USB; I forgot the one plugged into the TV.)

That's HDMI not USB. The USB is a micro USB port (it's a little difficult to see at first)