NoFilter will not work in your case because you are using Prompts which is a Query filter.
You need to make 2 queries in WebI.
In the 1st Query, use the Month Prompt and Drag the Month and Amount
In the 2nd query don't use any prompt. Drag thje Year and Amount.
Now create a measure variable with the following formula in 2nd query. And use this Variable instead of the actual Amount object.
VAR = [Amount] where ([Year] = FormatDate(ToDate(UserResponse(<Month Prompt Text>);"MM/yyyy");"yyyy"))
(Assuiming your month format is 03/2009. If not then use the correct format in ToDATE function.)