I highly recommend IE 7.
But anyway, let's stick with IE 6 since you're comfortable with it.
What we're going to do is:
Go into Internet Explorer > TOOLS > OPTIONS.
You should get the Internet Properties screen.
Go to the GENERAL tab and in the BROWSING HISTORY area, look for a button for SETTINGS.
Once in there, look for the Downloaded Program Files section. In there you will see an item named 'MSN Chat Control'.
Remove that item, close Internet Explorer, restart it, and then re-visit SparkPea and re-download the MSN Chat applet.
That should work. If it doesn't, we can go about it another way.