Single quotes (q) prevent variable interpolation. $sql2 contains the literal string $date1[$i], not its value ('2013-08-01 00:00:00.000'). Tip #2 from the Basic debugging checklist (print). Try qq

    my $sql2 = qq/SELECT Login_ID, AuditChrt_TimeStamp, Patient_ID
        FROM TopsData.dbo.AUDT_AuditChrt
        WHERE master.dbo.fn_sqlvarbasetostr(AuditChrt_TimeStamp) >= $d
+ate1[$i]    
            AND master.dbo.fn_sqlvarbasetostr(AuditChrt_TimeStamp) <= 
+$date2[$i]/;
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