There are several things required to host a site on your local machine besides DNS. DNS just does a lookup to send requests to the correct IP it is NOT A HOST!
Here is what you have to have in order to host a site.
1. Web Server on your local computer.
You can use IIS (microsofts web server), PWS (microsofts personal web server - visit Microsoft for details on getting them setup, not too hard but not easy either) or Apache a free webserver for linux, windows, or any OS. Currently Apache is the number one choice for most internet web servers!
http://apache.org you can also find easy to install packages for your computer. Once the webserver is working the DNS will point to that server and it will respond. You do have to have Apache or IIS working for them to send back a page!
2. An established web site for that Web server! You can build one and put the pages in the correct directory depending on the web server you are using. IIS uses a different directory than does Apache so all depends on the web server where you need to load your website!
3. You need to forward port 80 for the web server to work. That also means you need to change your routers default management page from port 80 to something else or it will not forward! You can change your routers port to 8080 or 81 etc using the routers setup pages.
4. You need to be sure your ISP (who supplies your connection) allows you to run a server! This is important because if they don't and you try you will find it simply won't work or you will find you will get dropped and have NO INTERNET for violating the terms of service.
5. You need your DNS pointed to YOUR IP which is all you have setup at this point!
In other words there is more too it than simple DNS entry!
ALL DNS DOES is point a name (your domain name) to your IP! It does nothing else nor can it.
GO to the Apache site, read and re-read it.
Once you understand what is involved you will see why paying a couple of dollars per month is well worth the expense for website hosting! Don't forget if your computer turns off, so does your website, if you cable or DSL goes down, so does your website. AND the outbound speed of your connection will limit the amount of users that can see your website at one time. Generally this is low on most home connections!