2008 QX56. Replaced battery. Dash and lights work. Car won't crank.

We jumped the new battery bc car wouldn’t start but lights worked. There were sparks

Battery cables hooked up backwards is not good! TEST ALL fuses with a test light or volt meter,ALL of them! you might get lucky and just find one or more blown fuses,but it is possible to have damaged the computer and or other components? no reason to have to jump start a NEW battery,unless the jumper cables were incorrectly hooked up backwards with the old battery.

Would the dash lights still work if fuses or other damage?

maybe,depends on what was damaged or which fuse(s) were blown!