The elevator on the stabilizer keeps going downward. Is there a way to correct it, so it is straight, and not drooping downwards?

When you say "keeps going downward" do you mean you have to add down trim in the elevator for level flight? If that's the case your stab or wing incidence is off. If it's a high wing plane shim the trailing edge of the wing up a tad to give it less positive incidence. I assume the stab is glued in and would be hard to adjust at this point. If it's a low wing plane you might have to modify the wing saddle a bit to raise the trailing edge. If that's not what you're referring to, please clarify your question with a bit more detail.

I am right now assembling my Sig Kadet LT-40 ARF. The elevator points downwards whenever I turn both sides of the elevator and stabilizer.

I really don't see the elevator drooping a problem if the control rods are not hooked up yet. When they are hooked up, the control rod should keep it level. But if it is not level when the rods are hooked up, then you can change that by usign your radio trim tabs or you can take the screw out of the servo and rotate it one spot.

"When ever you turn both sides of the elevator and stabalizer"?

What the heck are you talking about? Did you not glue the stab to the fuse?!

It would be a good idea to have someone in your town have a look. Are you going to a club? If not, definatly do.

Not sure if this is what you are talking about but I have seen the ele and stab droop downward or upward when the ele is deflected. Either the stab TE or the ele LE isnt straight. Cut it off and sand everything true and rehinge. When hinging just slip hinges in both surfaces and deflect surface both ways to ensure the right amount of gap between the two then ZAP em!(pink Zap that is) Hope this helps. If I am totally out of the ball park on what the problem is I'm sorry.......John