Yep, you can take the wood out one layer at a time, and get a good visual of what’s happening in there. Ideally you’d have raw wood at the top, black wood above the nozzles, charcoal at the nozzles and below, finer and finer down to the grate, where there should be some char dust and pieces about 1/2 to 3/4". You can save the various layers into different containers and put it back together again in order, it will work more or less the same.
Should look something like this:
I suspect your char is gone, or never existed. If you reassemble the charbed better/deeper than you found it, it will run better. You will likely need more charcoal.