You should not change the $new_style= area.
"In CSS style sheet
.catBoxHeading1---- line 913
.category-top-text--line 937
.sideBoxContent-----line 944"
.sideBoxContent will override selectors of equal importance that come before it, so you should have that first, and then the more specific selectors.
.category-top-text is the class of the link, so you can say
a.category-top-text {}
or #categories a.category-top-text {}
.category-not-selected is the class of the span inside the link, not the class of the link. If you don't want that to control the display, comment out its declaration.