Although many people who only have an internal function don’t think networking in general and LinkedIn specifically is useful to them, LinkedIn can also bring many benefits to them.
The most important one is that although many larger organizations have their own telephone and email directories, the information is very basic and limited to practical details. When people fill in their Profile on LinkedIn their colleagues might not only discover more about them, which allows better forming of teams, but also who is in their network.
As far as I know, there is no organization in the world which has that knowledge in an internal system. It is also very hard to do because they would have to ask every employee to list their connections and also update them when something changes. Since most people don’t have enough time to do their normal work, this is the first thing they will stop doing. The basic principle behind LinkedIn and any other social or business network is that everybody updates their own profile.
A last remark is that people who get things done, get more visibility, get promoted faster and will be the last ones to get fired. Getting things done also means that the job needs to be done, not that you have to do everything yourself. Finding the right people (fast) is crucial in this new economy of specialists. So use LinkedIn to find them outside AND inside your organisation.
To your success !