Investing money in securities is typically about as useful to the economy as stuffing it in a mattress.
When I buy $100 in Google stock, that money just vanishes as far as the economy is concerned (well, modulo the 30% broker fee, of course)
Again, this is wrong. For one thing, note that broker fees are on the order of fractions of a percent, not 30%.
When you buy Google stock from Google (i.e. during an IPO or subsequent public offering), that money goes to the company so that it can invest the cash in growth -- that means buying equipment, facilities, real estate, hiring and paying employees, etc. That money is most definitely in circulation.
Of course Google isn't selling stock right now because it has plenty of cash to fund growth and doesn't need to raise capital. So if you buy Google stock right now, you're buying it from someone else who bought it from Google (or from someone who did; the chain can be arbitrarily long). But the point is that you're buying it from someone. As it happens, I just sold a non-trivial (for me) chunk of Google stock; there's a check waiting at home for me which I'm going to spend on building a house (well, on covering some of the early incidentals; I'll get a loan for the bulk of it). That money will buy building materials, pay constructor workers, etc. That money is also definitely in circulation.
But what if you buy your stock from a big investment firm rather than from someone like me? Is it out of circulation then? Nope. The investment bank will take your cash and put it into something else... something, in fact, that it believes will be more productive than Google. At least that's true of the value-investing portion of the investment industry, obviously there are other segments that focus on arbitrage. The money managed by those segments is more debatable, but they do contribute significantly to liquidity, which translates to your ability to buy or sell Google stock on a whim.
There are some issues with the velocity of money in the US, which is a measure of how quickly it circulates. It's at the lowest point in decades. The fed has been pumping massive amounts of new money into the system, and it's not helping. I'm not enough of an economist to really understand the issues here, but the most sensible explanation I've seen is that circulation is reduced because people are using the money to pay down debt. We had a massive explosion of velocity fueled by an extravagant credit boom, but it was unsustainable. That unsustainability was a big part of the housing crash and the recession, but we still have excessive debt and the correction isn't over yet, so velocity stays low.