VLOOKUP will only find the 1st value that matches the look-up value (AI1). There is sort of a work-around I can suggest.
If A4:A32 are the total scores for each person, you can make it so that the totals are never exactly equal by adding an insignificant amount to each total.
Say A4 has the formula =SUM(C4:T4)
And A5 has the formula =SUM(C5:T5)
Change the formulas to this
A4 =SUM(C4:T4) + (ROW()*.0001)
A5 =SUM(C5:T5) + (ROW()*.0001)
This will add a small amount to each total of the row number of each cell times .0001. Then format each cell so they don't display the decimal values.
Because each person's total is in a different row, they will never be exactly the same but they will look tied since you've rounded off the decimals. Excel will still use the decimals when you do a look-up though.
When you do a look-up use this formula to get name of the person with the the largest score
=VLOOKIP(LARGE($A$4:$A$32, 1), $A$4:$T$32,2,FALSE)
2nd largest score
=VLOOKIP(LARGE($A$4:$A$32, 2), $A$4:$T$32,2,FALSE)
Hope that helps or gives you some ideas.
Alternatively, you could select A4:T32 and select from the menu Data\ Sort and sort on the column that has the scores.