There are three ways to check Event Logs on Remote Computer:
Using Eventvwr.msc snap-in
Using EventQuery.VBS
Windows Operating Systems (Windows XP and later) provide a built-in command line tool to check Event Logs on remote computers. EventyQuery.VBS ships with Windows. For more information on EventQuery.VBS and its syntaxes, please check out below URL:
http://technet.microsoft.com/en-us/library/bb490900.aspx
Using PsLogList.exe
Sysinternals (now Microsoft Sysinternals) guys have designed a tool called PsLogList. You can script this tool to check Event Logs or capture Event Logs in a text file. For more informtion on PsLogList.exe and to download PsLogList.exe, please see below URL:
http://technet.microsoft.com/en-us/sysinternals/bb897544.aspx
