In this case I think that you want to keep NAT inplace.
I think that the idea that the ISP may well be blocking your access to port 80. With this in mind I would try this with another port. For starters change the the port reference in the http.conf file from port 80 to some other number (such as 8080). Then restart the apache service. Now from inside the LAN you should be able to access the web site by going to:
http://192.168.0.6:8080
(if you opt to use a port other than 8080 substitute as necessary on the address above)
Once we have verified that this works than take a look at this instruction from no-ip
http://www.no-ip.com/support/guides/...k_port_80.html
[the TinyURL link if the above]
http://tinyurl.com/fdmuq
If I understand their instruction you should be able to mask non-standard port numbers.
Now you will have to set up port forwarding on the newly selected port on your DSL router sending port 8080 (or your selected port) to your web server (192.168.0.6). Now you should be able to access your page manually by typing:
http:\\[ip_address_from_IPchicken]:8080
If this works then you should be able to go ahead and try the no-ip hostname. (assuming that you followed the instructions on the link above)
Let me know how it works out.
Happy Hunting!