Thanks for the quick responses, guys.
I should add that I use this same banner under "advertising" in the CP and it works fine. The .swf file is in the main forum directory.
Here is the HTML that I have:
<OBJECT classid="clsid

27CDB6E-AE6D-11cf-96B8-444553540000"
codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"
WIDTH="468" HEIGHT="60" id="BMPF-wasabanner.swf">
<PARAM NAME=movie VALUE="wasabanner.swf">
<PARAM NAME=quality VALUE="high">
<PARAM NAME=bgcolor VALUE=#FFFFFF>
<PARAM NAME=wmode VALUE=transparent>
<EMBED src="wasabanner.swf" quality="high" bgcolor=#FFFFFF WIDTH="468" HEIGHT="60"
NAME="BMPF-wasabanner.swf" ALIGN="" TYPE="application/x-shockwave-flash"
WMODE="transparent"
PLUGINSPAGE="http://www.macromedia.com/go/getflashplayer">
</EMBED>
</OBJECT>
<!-- The following line is only needed once in the html after the last </OBJECT> -->
<script type="text/javascript" src="iefix.js"></script>