Hmm.. If I understand this correctly, from two inputs (name AND date), you want to produce one result (Important #)?
I'm not really expert in excel, but I'm pretty sure the index and match only works for 1 input - 1 output only.
On the other hand, a not very efficient formula can also be used by comparing one column at a time and using the IF function. It will look something like this:
=IF((INDEX(C2:C5,MATCH(B8,A2:A5,0)))=(INDEX(C2:C5,MATCH(B9,B2:B5,0))),INDEX(C2:C5,MATCH(B8,A2:A5,0)),"")
Where
A2:A5 is the "Name" column
B2:B5 is the "Date" column
C2:C5 is the "Important #" column
B8 is where you input the Name
B9 is where you input the Date
You can also use VLOOKUP which is a tiny bit shorter and probably easier to understand.
=IF((VLOOKUP(B8,A2:C5,3,FALSE))=(VLOOKUP(B9,B2:C5,2,FALSE)),VLOOKUP(B8,A2:C5,3,FALSE),"")
Not sure if this is helpful or workable; you might also want to read about the FILTER function in Googledoc. Too bad excel doesn't have this function.