Very Old Plane ???
I'm not an expert, in fact I'm also a beginner (still building my first plane), but about your description:
The way you described the stabilizer, it sounds like a V-Tail. And the 'damaged' covering might be the location where the control horns would normally attach to the elevators.
I think what you mean by the wing tapering is actually polyhedral (Taper is when the leading edge of the wing is not a constant angle, for example, the first few inches of a wing might represent a rectangle when seen from above, with the next inches making the wing look like a triangle, again, when seen from above).
Polyhedral means each wing is literally made of two parts, with the tip part having more of an upwards angle. I think all planes which have polyhedral don't have ailerons.
You said the front (nose) of the plane comes to a point. Does this mean that you cannot put in a propeller at the nose (ie. the nose of the plane is all in one piece and cannot be taken apart or move)? It's starting to sound like what you have is a sailplane (glider). Or if you can put in a propeller, it might be an electric powered glider. Strengthening the idea of a glider would be if the entire fuselage tends to be rounded and narrow.
The rectangular cutout with two holes is where you would put in a switch, to turn the airplane's receiver/servos on and off (this usually comes with the radio equipment you buy)
Here on RCairport, you can always try looking at different types of gliders until you find the one you have. Look at planes with the following characteristics: Handlaunch, Sailplane, Slope, and Thermal. Dur.
you might see a picture of what you have [img]i/expressions/face-icon-small-smile.gif[/img]
Other than that, you'll have to post a picture and someone might recognize it...