Since dnenrich uses permutation, the p-value (under the dnenrich null model) of the particular event you are testing is less than 10^-4 and even 10^-6. You can either report that p < 10^-6, or keep increasing the number of permutations until it gives you a better estimate that is not the lowest possible for that number of permutations. Of course, the latter may require you to wait for a while. You could however manually parallelize it by running 100 runs of 10^6 permutations each (10^8 permutations in total) and then:
1. multiply each run’s p-value by (10^6 + 1)
2. Subtract 1 from each result in 1
3. Add up all the results from step 2
4. Add 1 to the sum of events from step 3
5. Divide the result from 4 by (10^8 + 1)
Note that the whole thing here with 1 (adding or subtracting) is because dnenrich always counts the original observation of the event in question once in the numerator and once in the denominator.