While I am sure that you can make further adjustments to get this to work using a paragraph element, you are trying to create a navigational menu. So i dont recommend the use of a paragraph element. Semantics should be considered when you develop. For one, when a web spider tries to index your site, you want to help the spider understand the context of the data it's collecting.
If you are new to developing, you may want to consider learning HTML5. There are new elements such as the nav element as well as many others that bring semantics into the design.
In any case, if you are looking for a standard navigational menu, I have some examples that you are free to use and modify for your purposes.