Your template was slightly different from your initial post. In any case, it looks like you should be using the 'not all' option for the second filter group.
I have attached the modified template as per your original question, and the revised SQL look like
SELECT Nodes.Caption AS NodeName,
Nodes.Location AS Location,
Nodes.StatusLED AS Status_Icon,
SysLog_SysLogSeverities.SeverityName AS Severity,
SysLog.Message AS Message
FROM
((SysLog INNER JOIN SysLogFacilities SysLog_SysLogFacilities ON (SysLog.SysLogFacility = SysLog_SysLogFacilities.FacilityCode)) INNER JOIN SysLogSeverities SysLog_SysLogSeverities ON (SysLog.SysLogSeverity = SysLog_SysLogSeverities.SeverityCode)) LEFT OUTER JOIN Nodes ON (SysLog.IP = Nodes.IP_Address)
WHERE
( DateTime BETWEEN 42248.4111689815 AND 42248.4583333333 )
AND
(
(
(SysLog_SysLogSeverities.SeverityName = 'Error') OR
(SysLog_SysLogSeverities.SeverityName = 'Warning')) AND
(
NOT (SysLog.Message LIKE '%Up%') AND
NOT (SysLog.Message LIKE '%Down%') AND
NOT (SysLog.Message LIKE '%SYN ACK%'))
)