My 100-400 lens sounds like gears are stripped hear gears grinding when camera trying to auto focus - is there someplace to repaired and is it worth repairing

First try to use another lens If:
A. It does the same thing, bring your body to a camera repair shop.
B. It doesn't, you'll need to either buy a new lens or repair it at a camera shop.

This camera focuses the lens by sending an electronic signal to it. If you hear a clicking sound, the lens is receiving the signal, but not responding. I suggest you take the camera & lens to a local photo store & ask if they could let you mount another lens on the camera to see if THAT one works; if so, the problem is with your lens. A repair might cost as much or more than the purchase of a new lens (I'm assuming you have the "kit lens," which is the 18-55 mm lens) -- Amazon.com offers this lens for $100.
This is a wonderful camera; I use this with the same lens, and the D7000 with a larger zoom so I don't have to change lenses in the field. It's simple to use, does a great job. Only drawback I find is I can't use it with the older auto-focus lenses that need the focusing motor in the camera instead of the newer ones that focus in the lens, as yours does.
Probably worth repairing if it's the camera, but it sounds to me as if it's the lens that's giving you the problem.
Hope this helps!

How new is the lens? In or out of warranty? If out or warranty most likely solution is to find a Sigma authorized repair shop because your description sounds like the auto-focus motor gear has failed. If in warranty, check out Sigmaphoto.com for repair sites and also download the SIGMA_SERVICE_REQUEST.PDF. I've only had to deal with Sigma once on warranty matter and they were very helpful, provided UPS authorization for shipping on their nickel.

The focusing gear on that motor is stripped and the lens cannot focus. Not cost effective to repair. Canon will charge small fortune for the part and then the LABOR. Workiing on those small cameras is one royal PIA and labor intensive.

Usually the gears will strip the lens gears which tend to be plastics whereas Sony a cameras themselves have metal driven cogs....I once stripped a sigma zoom using an
A700 simply because the motor on that camera had no feedback on torque...put a different lens to check this out first...then check the faulty lens the cog is visible once you remove the rear mount.

sounds drastic but turn on cam and grab hold of lens to try to fully extend it manually. if you hear a crunching noise that means the gears are stripped. not worth repairing

You need to send it in for service. The more you use it with the "noise", the more you are potentially damaging the auto-focus drive mechanism of the lens. The sound you are hearing is most likely the gears and whatnot grinding away at each other because they were knocked out of place by the impact of the fall. I don't know how much this will cost, but I would say somewhere in the $200 range would not be unbelievable. Sorry I don't have any good news, but I have "bounced" a lens or two in my time.

I would take the lens off and then put it back on, being careful to align the registration marks on the lens barrel and the camera.  It should click into place quite firmly.  If this does not fix the problem, take it back for repair.

Take the lens off and rotate the focus ring, it should turn very easily with little gear noise.Try a different AF Pentax lens that you know is good.
I'm sure the lens is binding, take the lens to a camera repair shop for an estimate cost to repair.

Sounds like the camera is trying to focus if you hear sound when pressing the shutter halfway down or zooming. If the noise is a scraping or grinding sound, you might have debris stuck between the cracks of the lens and the camera body. This happened to me after i dropped my canon sd550 on the beach just once and it never recovered. Next to water sand has got to be one of a camera's worse enemy. Also, the lens might be cocked a bit which would prevent the camera from focusing and zooming smoothly. Try gently adjusting the the lens. Sometimes the slightest imperfection in the lens will throw everything off. Good luck!