You can build another wood fire on top of the coal. I wouldn't expect the wood fire to light the coal under it, but once you get the wood fire going hot, use some hardwood like oak if you have any, then sprinkle a layer of coal on top of the HOT wood fire. When the coal on top starts burning, sprinkle on annother layer of coal. Keep adding coal a layer at a time. When the coal you have added is all burning good, I think it will catch the dead layer of coal at the bottom.
If you havn't already done so, read the lighting a coal fire at the top of the Hand Fired Coal Stoves list.
Make shure you have a good draft going too. You can leave the ash door open a little while establishing the coal fire too. Make sure the hopper door, glass door and any above fire vents (if any) are closed. You can also put a sheet of aluminum foil over the barometric damper opening while lighting the coal to improve draft.
Stay with it and keep us posted. A lot of people struggle with their stoves and fires at first.