1. Since there are a possible of 1,323,253,342 different errors, please post the error when you have one.
2. Your syntax is all wrong. You can't put a where on it unless you use a SELECT.
So either do as Solution 1 says or change it to:
INSERT INTO TABLE1 (UID, LASTUPDATE, MODULEID,ENTRYNAME,NAME1,VALUE1)
SELECT NULL, 20150615050829, 2,'EEE','test','123'
WHERE NOT EXISTS (SELECT * FROM TABLE1 WHERE ENTRYNAME = 'EEE')