Study the file and figure out which section generates the two links in question - but be aware that once logged in, the "login" changes to "logout"+ links to the cart and checkout.

The relevant section is all within <div id="navMain"> ... and therefore you could, in fact, use css to hide it, simply by editing your stylesheet and adding either
Code:
display:none;
or
Code:
visibility: hidden
to the #navMain class,

The difference between them is that the former does not render the element at all and therefore takes up no space, whereas the second simply hides it but reserves the space. But remember the logged in state.