Cell content based on various conditions

Hello to all,
First let me apologize for the description of my problem. I am not very good at explaining things via the written word. My Excel knowledge is very limited and for that, I apologize as well.
Here is what I am trying to achieve. I am using Excel included as part of Microsoft Office 2010 Professional Plus running on Windows 7 Professional:

I have a row of three (3) cells.
Cell number one is either going to have a numeric value (currency formatted) or it will have nothing whatsoever (no number, no nothing!).

Cell number two is either going to have a numeric value (currency formatted) or it will have nothing whatsoever (no number, no nothing!).

I want cell number 3 to do/show the following based on the conditions note below:


If cell 1 AND cell 2 both have nothing in them, I want cell number 3 to show nothing whatsoever, even though there will be a SUM formula in cell 3.
If cell 1 AND cell 2 have a numeric value, I want cell 3 to perform a SUM of those two cells and display the results. However, if the result of that SUM is numerically ZERO, I want a ZERO to appear in cell 3.
If ONLY cell 1 or ONLY cell 2 has a numeric value in it, I want cell 3 to perform a SUM of those two cells and display the result, using the assumption that the cell with no value contains a ZERO, even though there is no actual ZERO entered in the cell.


I sincerely hope that explanation is somewhat lucid.
Any help or assistance you can give me would be most appreciated.
Regards.

Marvin,
Thank you very much for your amazingly quick response, as well as the accurate formula you sent me!
I am very impressed
Could I further push my luck and ask if I may request further help in the coming days?
Regardless, thank you very much!
Omicron