Error message.

If you use WICD (default with Debian) you cannot have both a static IP and WIFI, this is why WICD is useless here. Not sure why you cannot set the static IP address, the IP a listing still shows that it has not been setup (this is why you cannot ping the card)

Did you save the network setting?

The "unmanaged" suggests that the /network./interfaces file has been edited, was this ever done?

I've selected wifi while installing Debian.

Is there a way out of it? Can i disable wifi in bios or what else can i do?

Should i try and reinstall Debian with LAN?

Are you sure WICD has been removed?, that is did you install network manager
and remove wicd with:

sudo apt-get remove wicd wicd-gtk

?

I think you may have dueling network managers

I reinstalled debian 3 hours ago.
Only thing i did is updated it and LinuxCNC, no other installations or things done with OS.

But how and what to do about it?

Delete WICD since it cannot setup static IP address properly and install net manager.

My appologies I didn't realize you changed the network manager because of the WIFI. I still think you should at least be able to connect to the card using the preinstalled network manager though.
I let PCW handle this.

Ok guys to prevent any confusion. 
when i started setting up MESA yesterday i did installed second network manager. I used instruction from attached image. After i've added second manager and removed WICD everything stopped working. I could not even connect WIFI and there were no other networks available.

Yesterday evening i got tired and simply reinstalled Debian so everything is back to square one. The only thing i did is selected WIFI while installing it. I don't need wifi so first i will try to reinstall Debian without it.
I want to keep everything as basic as possible. If it doesn't helps than i will try with new manager.

So i've reinstalled Debian and switched wifi off from the bios.

See attached screenshot. Still no luck.

Still same no mesa 7i76e found.

Did something actually change in this picture? I need to remove WICD and install another manager now?

From what i understood it is important to adjust jumper W3 in position UP. I did so and also tried everything in position down. Do i need to adjust any other jumpers except W3?

P.S. Also i found this instruction:

www.rainydayprojects.ch/linuxcnc/mesa-7i...7i76e_setupguide.pdf

​​​​​​​Is it actually relevant? Maybe i also need to install firmware? 

1 WICD cannot setup a dynamic + static IP setup, this is why it must be replaced with netmanager.
2. Not sure but your error messages suggest that the first time you tried, WICD was still installed (the "unmanaged" message)
3. I would first get the static IP address setup and verified with "ip a" first without worrying about WIFI, that is, lets solve 1 problem at a time.
4. W3 sets the 7I76E IP address to 10.10.10.10. This is the suggested address to avoid routing issues with typical WIFI/Local network NAT ranges
5. This is not 7I76E or firmware related, unless your host shows a 10.10.10.XX IP
address with "ip a" (where XX is not 10,1,255 or 0), you will not have communication