Nice go at a one-liner solution, but I think this will give a different answer, it will print if fewer than three of the replicates have a '0' value.
To find only rows with at least three replicates that are non-zero, this awk command should work:
awk 'BEGIN{FS="\t";OFS="\t"};{count=0;for(i=2; i<6; i++) {if($i!=0) {count++}};if (count>=3){print $0}}' boogens.txt