Okay, removing all of your class reference stuff, it looks like firstRow is not an array reference. Add this to your code, right after your first line in the new statement.

 die "Ack!  That's no reference. IT'S A MAN BABY\n" unless(ref $firstR
+ow eq "ARRAY);
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That will let you know if you're actually getting a reference to an array. Watered down, without the object stuff, this code works for me:

use strict;

my @AoA;
push @AoA, [1..40] for(1..20);

print ref $AoA[0]."\n";
print "".(ref $AoA[0])."\n";
print $AoA[0][1]."\n";

Producing (correctly): 
ARRAY
2
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This looks different than your code in a couple of places. First off (and apologies for the offtopic-ness, but it may simplify your code a bit), since you never use $row, you can simply your for statement to be:

for(1..$rows)
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Ahh, a fellow C programmer ;). This is a range, and will be interpreted correctly by the for statement. Pushing the 1..40 or (1..$rows) in array context works fine for making 2d arrays.

Your best buddy here is ref. It will tell you whether you can make something into an array or not. For instance... if you

print ref $obj->{AoA};
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...it will tell you whether you can use it as an ARRAY. Now if you

print ref $obj->{AoA}[$row];
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...that will tell you that it's either a SCALAR or (more likely) not a reference (a blank string) in your previous trouble. This means that it can't be dereferenced as an array.

Hope that it's enough to get you started!

    --jb