I need help with a script to pull information from AD

I found a script that is suppost to login and logout information.  I need to find login and logout information about a user and the event logs don't go back that far.  I would think that AD would have that information.  Here is the script that I have.  I am useing Server 2008 R2 SP1.  I would like some help to figure this out.  I know that the computer is wrong but, I don't know have to intergrate the user.  I will be using the SAMname.  The information is from a month back.  I am not sure how long AD keeps that information.
 

$UserProperty = @{n="User";e={(New-Object System.Security.Principal.SecurityIdentifier
 $_.ReplacementStrings[1]).Translate([System.Security.Principal.NTAccount])}}
 $TypeProperty = @{n="Action";e={if($_.EventID -eq 7001) {"Logon"} else {"Logoff"}}}
 $TimeProeprty = @{n="Time";e={$_.TimeGenerated}}
 Get-EventLog System -Source Microsoft-Windows-Winlogon -ComputerName $Computer name goes here | select $UserProperty,$TypeProperty,$TimeProeprty
 

Thanks for your help.