How can I ignore BLANK or ZERO cells in a MIN/IF function??

I AM TRYING TO USE AN IF FUNCTION TO LOOK FOR THE LOWEST (MIN) NUMBER IN A RANGE OF CELLS THAT IS LESS THAN MY SELECTED CELL. EXAMPLE: =IF((MIN($F$4:$F$18)<$I$4),TRUE,FALSE). Lets say that $I$4 equals 60, and the lowest number in the F4:F18 array is 61. This should return FALSE, but since some of the cells in F4:F18 have "0" or are Blank, the formula returns TRUE even though I DO NOT WANT IT TO! However, I must have some "0" or Blank cells in this F4:F18 cell range.

So, I tried to combine AND with IF to argue something like this: =IF(AND(MIN($F$4:$F$18)>0,MIN($F$4:$F$18)<$I$4),TRUE,FALSE). This way I get TRUE if values in my cell range are "greater than 0" AND less than my selected cell ($I$4). PROBLEM IS THAT this blasted Excel will only return FALSE, even though both these arguments are TRUE!! How can I get this argument =IF(AND(MIN($F$4:$F$18)>0,MIN($F$4:$F$18)<$I$4),TRUE,FALSE) to return TRUE when some cells in my array have a "0" in them?

THANK YOU IN ADVANCE TO ANYONE WHO CAN HELP ME RESOLVE THIS!