Or does the internet go down too? Have you tried a laptop to see if the internet is up? At least the internet modem would have to be battery too I guess.
I have a device that turns car battery(s) into AC. It is hefty enough to run my big old TV during our power outages (but dang the cable is out too). A computer and mixing board should be real doable. It's fairly heavy (metal heat sinks on those solid-state diodes) but still luggage-able as it's size is like a big laptop.