Reporting on user's log in/out times in Active Directory without using the event log

Do you have a SQL server there?  You could create a database on the server with a table called emp_logins with the columns
userid
login_off_datetime
login_or_logoff

Then run this script as part of the user's logon script

Set wshNetwork = CreateObject("WScript.Network")
Dim OdbcDSN, connect, sql, resultSet, strUsername

strUsername = wshNetwork.UserName
OdbcDSN = "Driver=SQL Server;Server=YOURSQLSERVER;UID=someuser;PWD=somepassword;Database=somedatabase"
Set connect = CreateObject("ADODB.Connection")
connect.Open OdbcDSN

sql="insert into emp_logins (userid,login_off_datetime,login_or_logoff) values ('" & strUsername & "',getdate(),'I')"

Set resultSet = connect.Execute(sql)

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And this script as a user logoff script

Set wshNetwork = CreateObject("WScript.Network")
Dim OdbcDSN, connect, sql, resultSet, strUsername

strUsername = wshNetwork.UserName
OdbcDSN = "Driver=SQL Server;Server=YOURSQLSERVER;UID=someuser;PWD=somepassword;Database=somedatabase"
Set connect = CreateObject("ADODB.Connection")
connect.Open OdbcDSN

sql="insert into emp_logins (userid,login_off_datetime,login_or_logoff) values ('" & strUsername & "',getdate(),'O')"

Set resultSet = connect.Execute(sql)

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To run a report just execute the query in SQL Query Analyzer

SELECT * FROM emp_logins WHERE userid = 'SomeUserName'

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Make sure you update the values in the script for
YOURSQLSERVER
someuser
somepassword
somedatabase