In your first sentence, "West Virginia University" is a proper name (proper noun phrase), while in the second sentence, the university is not specified. It is just a university (common noun) located in Virginia, and so it should not be capitalized.
The likely cause for your confusion is the fact that news headlines usually don't follow conventional grammar rules, and abbreviate titles, e.g. by leaving out articles.
As OP Costa points out in the comments, if the second headline was written in accordance with conventional grammar rules, and not headlinese (as pointed out in the comments by Kevin), it may have read something like this:
Students sued a Virginia university after a campus feminist group member was killed.