Could anyone recommend me the best service center in Cairo downtown for repairing my Nikon D5100 camera?

When you connect a lens from another firm, or an old one without a chip, The camera can't work in the automatic settings. So not one scene and also you can't use the A, S, P and Auto. Really only manual is possible. And you have to dial in everything. like shutter time and you have to set focus and Aperture on the lens.

there are special repair centres fir water damage. Not sure you can find one close to you. You could try to put the camera in a bag of rice, and contact a Nikon certified service centre immediately. First ask them if they can repair and then what it will cost. Could be expensive, so i think you should start saving for a new camera.

Open your appuatue set your ISO to 200 or 1600 what ever it needs

You can't pop up the flash in the Auto mode. In this mode the camera decides whether to use the flash or not.

Try switching to one of the PSAM modes. Does the flash then pop up when you push the flash button?

do you have it set on automatic focus and if so you may have a bad lens
push shutter buton half way down when select in auto it will focus it for you if that don't work send lens in

This is not a DIY job, you need to take your camera to a Nikon camera service center for repairs.

No. This lens lacks an autofocus motor, relying on the camera to have one. The D5100 lacks an autofocus motor, relying on the lens to have one. Adding a battery grip does not change this situation.

The D5100 only autofocuses with lenses having an internal autofocus motor. Nikon designates such lenses AF-S, Sigma calls it HSM. Lenses without the motor will only autofocus with the larger and heavier Nikon cameras such as the D7000.

Quantaray makes lenses with a variety of mounts for a variety of cameras. A lens with a Sony mount, for example, will not fit onto a Nikon camera. Assuming the lens has a Nikon mount, it will fit on the D5100. However, the D5100 requires the lens to have an autofocus motor. If the lens does not have such a motor then it will not autofocus. It will still work fine as a manual focus lens.

I have seen this a few times on d5100 s in all cases there was no home grown fix. when the lens and camera won't talk, i.e. does not know what apertures are available or focus control. I would try a local repair service, before sending it to NIKON USA, they have a flat rate fee depending on the level of repair. and some local guys will just charge you for the job.

: things to try, master reset, press the two buttons that have a green dot by them on the top of the camera for 2 seconds
update firmware.
power off battery out sit for bit and hope it works.
sorry about your nikon,
ps the D850 is due any day.

You best solution is Nikon authorized repair station. You are asking for an easy solution for a costly complex camera will worth having repaired with Nikon who has the experience and computer test equipment to diagnose the problem.