Are you specifically looking for http access, or general computer access?
If you're looking for general computer access, here is what I do.
I use Remote Desktop (native to Windows 7 machines, except Home Basic, I think), using a free DNS redirect from No-IP, and forward the RDP port directly to my home computer's IP address. Right now it sounds like you've accomplished the free DNS redirect fine, but you haven't forwarded the appropriate port to your computer's IP, so it is loading the remote management side instead.
RDP is pretty robust, and when coming from one Win7 box to another, it's fantabulous. I also have XtraLogic's RDP client for Android on my BIONIC, and it works pretty well, much better now that I'm n 4G land.
Others might say there are other alternatives - VNC (used plenty of times, works pretty well), Team Viewer (used for the first time a couple of nights ago to help a fellow androidian get back to stock on his BIONIC), (both of which are free) and LogMeIn (not free, IIRC), and others.