This article explains why having a "complete" LinkedIn profile is not enough.
One thing LinkedIn is good for is being able to supply other people with your information. That is, you can list your LinkedIn affiliation on your vitae, or your business card, or verbally ask someone to seek you out there.
Another thing LinkedIn is good for is being able to contact others you are connected with. For example, you can see that someone you know has a connection to someone you would like to know--you can request an introduction.
But how can you increase your chances of what is perhaps the holy grail--a hit on your profile without these person-to-person transmissions, with an opportunity, solely through the attractiveness of your own profile?The link above gives a run-down of how to set the conditions for the "out of the blue" contact. It's not a promise, by any means, but an explanation of the algorithms and conditions which can make that possible.