That equation should have a colon (not a semi-colon) in the middle. Like this:
=sum(a1:a17)
The colon indicates a range, i.e. everything from one cell to another. The way I do a running total is:
Say your row totals are in column F. Then in G1 type =f1. Then in g2 (next row down, same column) type =f2+g1. That is, the total of the cell above, and the cell to the left. After that just copy and paste that cell (g2) down, one row at a time. Excel will figure it all out.
The approach you are using to add each row (by sport) across should work to add each column (day) down. Is the problem in the format of the cell that contains the column total?