It appears to me that the dialog is actually opening just fine, but it's behind the powershell console window. Unfortunately it doesn't show in the taskbar, so there's no indication that it's there unless you move the powershell window or Alt+Tab. It also appears that the ShowHelp workaround didn't have any effect for me.
EDIT Here's a way to do do it using your secondary-form idea. The basic idea is to create a new form which opens the OpenFileDialog from inside its Shown event. The key is calling Activate on the form before opening the dialog, so that the form comes to the front and the dialog appears. I moved the form offscreen by setting the Location to an offscreen value, but you could alternatively set Form.Visible = $false from inside the Shown event.
[void] [Reflection.Assembly]::LoadWithPartialName( 'System.Windows.Forms' )
$ofn = New-Object System.Windows.Forms.OpenFileDialog
$outer = New-Object System.Windows.Forms.Form
$outer.StartPosition = [Windows.Forms.FormStartPosition] "Manual"
$outer.Location = New-Object System.Drawing.Point -100, -100
$outer.Size = New-Object System.Drawing.Size 10, 10
$outer.add_Shown( {
$outer.Activate();
$ofn.ShowDialog( $outer );
$outer.Close();
} )
$outer.ShowDialog()