I have about 6 columns of data, but only 3 are important in what I'm
trying to find.  Here is an example of my spreadsheet:

Score   FY      Awarded
131     2001     1
145     2001     1
120    2001      0
256    2002      0
344    2002     1
138    2002     1
111    2002     0

Rows 5 through 49 have these data.

etc... up until FY 2006.  The data are assorted by FY ascending.  1 in
the Award column means it was awarded, 0 means it wasn't.  I want to
find a formula, if possible, that will find the minimum score that was
awarded in each FY.  I was able to do it with this:
=DMIN($F$5:$K$49,"Score",F1:K2) where the criteria are "=2001" or
whichever FY I am interested in and ">0" for the FY column.  But, this
is messy because I have to either set up several database headers, or
manually go in and change whichever FY I am searching for.  Clearly I
can do this all manually, but I want to find a formula where all I have
to do is change the FY in the formula to get my result.  I've also been
trying things like:

=MINA(IF((AND($H$6:$K$49=2001,$K$6:$K$49>1)),$F$6:$F$49))

Thoughts?  Is what I'm trying to do even possible?  Or should I just go
in and do it all manually...

Thanks in advance