Vb.net – I would like to know is there a 64 bit version of advapi32.dll

There isn't much to go on here, but it sounds to me like the service account doesn't have the required access rights to the database.

If you installed the service to run under Network Service or Local, create an account on the server that has access to the database and change it to use that service.

To give Network Service read permission on the EventLog/Security key (as suggested by Firenzi and royrules22) follow instructions from http://geekswithblogs.net/timh/archive/2005/10/05/56029.aspx

1. Open the Registry Editor:
   1. Select Start then Run
   2. Enter regedt32 or regedit

2. Navigate/expand to the following key:

   HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Eventlog\Security

3. Right click on this entry and select Permissions

4. Add the Network Service user

5. Give it Read permission

UPDATE: The steps above are ok on developer machines, where you do not use deployment process to install application.
However if you deploy your application to other machine(s), consider to register event log sources during installation as suggested in SailAvid's and Nicole Calinoiu's answers.

I am using PowerShell function (calling in Octopus Deploy.ps1)

function Create-EventSources() {
    $eventSources = @("MySource1","MySource2" )
    foreach ($source in $eventSources) {
            if ([System.Diagnostics.EventLog]::SourceExists($source) -eq $false) {
                [System.Diagnostics.EventLog]::CreateEventSource($source, "Application")
            }
    }
}