OK, I need syntax help...

I have a column, F3:F44 where I enter data. Cell F45 will subtotal these numbers, but if there is no data in the column, I want cell F45 to be blank. I'm running into syntax problems with the OR command. My original function looked like this,

=IF(OR(F3=0,F4=0,F5=0...F44=0)=TRUE,"",SUM(F3:F44))

Yes, I actually typed in every cell for F3->F44. The problem is that I'm entering to many arguments for the OR function. What, then, would be the syntax for the following idea? (or any other way of accomplishing the same end)

=IF(OR(F3:F44=0)=TRUE,"",SUM(F3:F44))

Any help is much appreciated!