Can't give you an example, as generally power is also a form of wealth, I guess.

Wealth can buy almost anything, including hard power. But in some cases is not enough. Imagine, for example, that you have a considerable amount of fiat money, let's say, 20M. It'll bring inevitably some people to your side (employees, "friends", politicians and so on). On the other side, it can bring some enemies too.

Then, the ability to balance the number of tolerable "friends" and enemies will ultimately determine you power. If you have a lot of money and assets but no allies, you're doomed.

You can have billions, but if someone has just a few millions and a small army, you're doomed as well. Just notice how militia and cartel grows so fast, they certainly must be helped by other people with enough "soft" power (bureaucrats and scum).

I don't know anyone rich enough that hasn't a certain amount of power, or the contrary. Perhaps gurus and sect leaders, some of them have a little influence on a particular sphere, but not broadly.