Can YOU make a case for it? Sounds like you want it because LINQ is fun. Other people are mentioning features that are fun. I've always had a problem selling fun features to management because they aren't very compelling reasons to potentially disrupt an environment.
Honestly, it really depends on what you are using C# for. Are you a web developer, system admin, something else? Taking a general approach, I would use the following selling points (you will need to do some work to prove these things):
- Zero-disruption for end-users when upgrading. Upgrading to the new version will be seamless and we will have a thoroughly reviewed test plan for updating all clients to this version. All of our old applications that require .NET 1.x or .NET 2.0 will still work perfectly.
- Programmer Efficiency. You could mention how more of the Windows API is wrapped by .NET classes, thus making programmer more efficient because they don't have to P/Invoke as much. LINQ makes your more productive because of x, y, and z. Lambda expressions make you more productive because of x, y, and z.
- Ease pains of future OS migration. Moving to WPF now will prepare us for Vista/Windows 7. We won't have to migrate applications using the now deprecated "Windows Forms" to WPF, because we will already be using it.
- More applications purchased from 3rd parties will require it, so we will have to upgrade sooner or later.
In the end, you need to prove that at the very least, this move will not cost you money in terms of increased support or testing costs. If you can show it will make you be more productive and it will be a rather painless switch, then you will get your wish.