The only reason this outage happened is because you don't have a generator. You can power your node and router from a small 12V inverter on your car and periodically start the car to recharge the battery. If you have an extra battery lying around, you can run the inverter from that and charge it with jumper cables.

If your internet is over cable TV lines, you probably won't have internet because the amplifiers are powered directly from the power lines with no power backup. You'd need to use a hotspot. DSL internet generally is battery backed by the CO, so all you need is to power your modem. Obviously starlink will work fine, but you'll need a larger inverter to power it, at least 300W.