Two industry experts who differ on the agreement answer your questions. The chances are somewhere between slim and none. Perhaps a super nice Linux browser might be something that would sell. The chance of a startup competing in the general purpose browser market is effectively zero today. But you'd be crazy to even enter that market right now.
Browsers are free, so there's no money to be made in introducing a new one.
There are some special purpose browsers that are oriented toward special uses or industries that are available. Spyglass is a notable maker of browsers for devices that are too small to support a full Navigator or Internet Explorer. And there are some free alternatives like Opera that target older PCs. But these are mainly niche products. As far as the competitive issues of market dominance, that is a very big question.