Is there a way to use a Case statement to read from one field and change another field?
I don't see why you'd even need a case statement for this. Assuming your table is called myTable in the dbo schema (you didn't specify, but it isn't particularly important) and we're talking about updating the field in the same row.

UPDATE dbo.MyTable
SET Form_Factor = 'Server'
WHERE Category LIKE '%Server%'


Msdn link: Update with Where

I don't see how any database professional can be stumped by this though.. unless the problem is much more complex than you are letting on.