This I reckon is the correct way to write your query:
select T2.COL1, T2.COL2, T1.COL1, T1.COL2, T1.COL3
from T1
join T2
on T1.COL4 = T2.COL3
where T2.COL4 != 'data1'
and T1.COL1 is not NULL
and T1.COL5 is not NULL
and T1.COL6 = 'data2'
AND NOT EXISTS (SELECT 1 FROM T3
WHERE T3.COL1 = T2.COL1
AND T3.COL2 = T2.COL2
AND T3.COL3 = T1.COL1
AND T3.COL4 = T1.COL2)
Check the results against the SELECT part of your original.
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden