The DMZ setting in home routers only affects INCOMING connections. If you are browsing the Internet, you are normally initiating OUTBOUND connections to web servers, which are unaffected by DMZ settings.
DMZ settings could affect other "server" functions your PCs are performing, such as hosting games, and P2P, video, and IM functions. But, generally speaking, if you didn't have to "open ports" on your router to get these functions to work in the first place, then your DMZ setting won't matter.
Note that enabling DMZ GREATLY increases the risk of attack on whichever PC you point it to. Be sure you have a PC firewall enabled and that your OS and your web-enabled applications are fully patched.