Returning # Of Columns With Non-null Value

Using SQL2000. I want to return the # of columns with non-null
values. Here's my query so far:

select
case when Dx1 is not null then 0 else 1 end +
case when Dx2 is not null then 0 else 1 end +
case when Dx3 is not null then 0 else 1 end +
case when Dx4 is not null then 0 else 1 end as DxCount
from tblClerkshipDataClean
where PalmName = @PalmName

There are 7 rows for the particular PalmName I'm using. The query
returns a result of 7. However, there are 25 values in Dx1 thru Dx4
so the query should be returning 25.

What am I doing wrong here? Thanks in advance.