An autogyro is not a better example. I wanted a more direct example of motive, mechanical power (i.e. what you already accepted as power, as I didn't at the time feel the need to teach you basic physics) producing lift than a fixed-wing aircraft, which does it by producing thrust, which moves the aircraft, which causes airflow across the wing which then produces lift. The helicopter just uses power to movement of a wing that produces lift. You then come up with an autogyro, which does use power to produce lift but in an even more roundabout way than a fixed-wing aircraft!
Your examples get more idiotic by the moment. When you find a helicopter with a rotor diameter the same as the propeller on the arrow, then you'll have your comparison. An autogyro has a propeller which achieves thrust in the same way as the arrow, and is therefore a better comparison, while the rotor remains in a state of autorotation providing lift...just as the arrow's fixed wing produces lift.
Put a propeller on the arrow the same diameter with the same blade area and properties as the rotor on the helicopter, and find a way to get it in the air without striking the prop...and you'll have a rough comparison. However, you won't be able to make one between the arrow as it stands, and a helicopter (particularly with respect to gliding); no comparison between lift, thrust or drag.
Are you thick enough you can't tell the difference between an airplane and a helicopter? Someone allows you to pilot an aircraft in that condition?
You really don't understand what power is, do you? I say again: power is the rate of conversion or transfer of energy. Nothing more, nothing less. It does not require machinery. It can come from the burning of fossil fuel, the falling of a weight or the differential heating of the Earth's surface. It's still power!
Also irrelevant in light of your assertions that an aircraft with a limited glide ratio couldn't fly on the power provided by a light airplane engine. That was your assertion before...which is wrong. In fact falling back to your ther-world helicopter example...you're not going to find a helicopter with an impressive glide ratio in autorotation (or for you, an autorotative-powered state, if you wish)...never the less, without needing an ungodly amount of engine power, it flies, hovers, and returns to land intact.
You asserted that an aircraft with a low glide ratio couldn't do it...it was this ridiculous assumption which kicked off the discussion, and the fact of the matter is that the glide ratio isn't necessarily indicative of what the aircraft can do under power. Several examples have been provided of aircraft with power to weight ratios approximating most light airpalnes in which glide ratio was very poor with power reduced by varying percentages...yet the airplanes managed to do very well under power.
Again, to the point of the original poster (which you never found, and what bit you did, you apparently lost very early on)...the glide ratio isn't particularly important; it's what occurs at the end that counts. That applies every bit as much in an airplane as in a helicopter.