I have only used IE 6 and 7 for Lansweeper.
When you click on ping does that work?
When you put in just "notepad.exe" does it open?
You said you changed the settings, but just double checking. Bring up Internet settings, click on security, click on "Local Intranet", click Custom Level, then make sure all ActiveX settings are set to enable.
I'll see if I can get IE8 and test Lansweeper myself.