SQL Server Query to EXCLUDE Friday and Saturday of the week & 4PM to 8PM all the days of the week
Assuming that DATEFIRST = 1 (Monday), you can use datepart(dayofweek) to avoid Friday and Saturday and for the time part, I've edited my previous answer due I think you said 8PM, I supposed 08:00:01 must be included in the final result.


declare @events table (Name varchar(20), ProcessStartTime datetime, Status varchar(20));
insert into @events values
('Name1', '2017-04-01 17:00:02', 'SUCCESS'), -- (Saturday)
('Name2', '2017-04-02 21:00:02', 'SUCCESS'), -- (Sunday)
('Name3', '2017-04-03 01:00:02', 'SUCCESS'), -- (Monday)
('Name4', '2017-04-04 05:00:02', 'SUCCESS'), -- (Tuesday)
('Name5', '2017-04-05 18:00:02', 'SUCCESS'), -- (Wednesday)
('Name6', '2017-04-05 15:00:02', 'SUCCESS'), -- (Wednesday)
('Name7', '2017-04-06 23:00:02', 'SUCCESS'), -- (Thursday)
('Name8', '2017-04-07 15:00:02', 'SUCCESS'); -- (Friday)

SET DATEFIRST 1

SELECT Name, ProcessStartTime, Status
FROM   @events
WHERE  datepart(DW, ProcessStartTime) NOT IN (5,6)
AND    (datepart(hh, ProcessStartTime) &lt; 16
       OR    
       ProcessStartTime &gt; DATEADD(dd, DATEDIFF(dd, 0, ProcessStartTime), '08:00:00'))

GO


Name  | ProcessStartTime    | Status 
:---- | :------------------ | :------
Name2 | 02/04/2017 21:00:02 | SUCCESS
Name3 | 03/04/2017 01:00:02 | SUCCESS
Name4 | 04/04/2017 05:00:02 | SUCCESS
Name5 | 05/04/2017 18:00:02 | SUCCESS
Name6 | 05/04/2017 15:00:02 | SUCCESS
Name7 | 06/04/2017 23:00:02 | SUCCESS


dbfiddle here