If you have hit the new Commercial Use Limit on Search on LinkedIn, your search results screen will look like this - the first few results are shown and the rest are blurred:
Amazingly, the "commercial" search limit affects even the search for your first level connections!
(If you have a basic or a job seeker account and are doing lots of searching, but don't see the limit, it may be that your account has not been "upgraded" yet. In this case you won't see the full profiles for the 3rd level connections either.)
Here's how to un-blur the hidden profiles - and see this instead (!):
Step-By-Step Instructions for the Unblurring Tool