Confusion on Fixture WIring Help
OK, after turning off the breaker, take the two white wires on the right, with the orange and the yellow wire nuts, and twist them together. Turn the power back on and check the other rooms for power. If they have it, get your voltage meter and check between the ones you just twisted together and the white wire with the tape coming from the switch. If you get some on/off readings while operating the switch, then turn off the power again and hook the black wire from the fixture to the white taped wire from the switch and the white wire from the fixture to the two you twisted together. Turn back on the power and text everything. Turn off the power again, tuck the wires back into the box  and screw in the fixture.

FYI, that group of black wires contains the hot from the breaker, the hot to the switch and the hot to the other rooms.