Something like this maybe.
I've had to make a few assumptions, such as what exactly you mean by "within 1 minute", and I've also assumed that tables TableA and TableC do not store times in the Timelogged columns to a higher precision than 1 minute. Also, are the values of the Timelogged columns in the TableA and TableC tables unique?
--UPDATE C SET Value = 1 /* Uncomment UPDATE when tested */
SELECT C.Timelogged, C.Value /* Comment out SELECT when tested */
FROM TableC AS C
JOIN TableA AS A ON (C.Timelogged = A.Timelogged)
WHERE EXISTS (
SELECT 1 FROM TableB AS B
WHERE (B.Timelogged >= A.Timelogged)
AND (B.Timelogged < DATEADD(minute, 1, A.Timelogged))
)
AND (C.Value = 0)
The update will be faster if there are indexes on the three Timelogged columns.