How to filter a table using awk

I was wondering how to filter a table with several columns based on a specific value in each of the columns of interest. I have this example here:

Chr1    16644   0       0       1       1
    Chr1    16645   0       0       1       1
    Chr1    16646   0       0       1       1
    Chr1    16647   0       0       1       1
    Chr1    16648   0       0       1       1
    Chr1    16649   0       0       1       1
    Chr1    16650   0       0       1       1
    Chr1    16651   0       0       1       1
    Chr1    16782   0       0       0       0
    Chr1    16783   0       0       0       0
    Chr1    16784   0       0       0       0
    Chr1    16785   0       0       0       0
    Chr1    16786   0       0       1       1
    Chr1    16787   0       0       1       1
    Chr1    16788   0       0       1       1
    Chr1    16789   0       0       1       1
    Chr1    16790   0       0       1       1

And I would like to remove all the rows containing a zero in all of the columns 3,4,5,6. I have tried it as such

cat STARsamples_read_depth.txt | awk '$3 != 0 && $4 != 0&& $5 != 0 && $6 != 0' | less

But it removes also the rows where only some of these columns have a zero, not in all four! Is there a way to do it? thanks Assa