Yep, IIS or some other such service seems to have been causing the issue.  I removed that particular IP address from my network settings so Windows would know nothing about it and now the requests seem to be getting through to the iDRAC6 Express card just fine on that IP.
I just colocated a server (Poweredge R515) with an iDRAC6 Express card and I can't seem to get the web interface for the card to come up. I changed the IP/subnet/gateway address info for the iDRAC6 Express card using the Server Administrator and setting it with an extra IP I have with my colo, but when I go to [URL] it just says "problem loading page".  On my home network, obviously with different address info in there, it worked fine.  I've checked the address info now about 10 times and it looks right, so I'm stumped. Any ideas?
iDRAC6 Express Problems