Instead of

$new_monthly_page_hits{$page}=@row;
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I think you want to do

$new_monthly_page_hits{$page} = $row[0];
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to actually store the number you got back.

But why do so much work in Perl when you can have the DB do the work?

select page,count(page) 
from counter_monthly
group by page
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will return you a list of pairs (page, hitcount). If you only want a very small subset of the whole database as not all pages are of interest to you, then your approach might be faster though.