I think it's probably easier to just use grep to filter the list while copying it... Something like:

my @tableData =
    grep ref($_) eq "ARRAY" &&   # make sure we have an arrayref
         $_->[0] =~ /\S/    &&   # first  cell non-empty
         $_->[1] =~ /\S/,        # second cell non-empty
    (
        ["Hardware A", "Total Cost A"],
        ["Hardware B", "Total Cost B"],
        ["Hardware C", ""],
        ["",           "Total Cost D"],
        [" ",          "Total Cost E"],
        ["Hardware F", " "],
        [" ",          ""],
        ["Hardware H", "Total Cost H"],
    );

# to print out
use Data::Dumper;
print Dumper \@tableData;
[download]

(The literal strings I put in above can of course also be variables...)

Or, if you wanted to use $some_data, as you declared it, it would look like

my @tableData =
    grep ref($_) eq "ARRAY" &&   # make sure we have an arrayref
         $_->[0] =~ /\S/    &&   # first  cell non-empty
         $_->[1] =~ /\S/,        # second cell non-empty
    @$some_data;
[download]