If all the expressions equal zero (or null) and you have Suppress Zero Values checked, then the line won't show up. All expressions have to be zero for the line to be suppressed.
For the lines that are showing a value, you could use something like:
If(TOTAL_VALUE > 0, RegExpression)
Use whatever logic for the total value that you need per your application. For RegExpression, put in the expression that you are using. If your TOTAL_VALUE is zero, it will resolve to null. If you do this on all of your expressions, the line will be hidden unless that TOTAL_VALUE is greater than 0.