Errors preventing LinuxCNC from starting.

You do not set the host address to 10.10.10.10 (that's the address of the FPGA card)

I would set the host address to 10.10.10.1 and netmask to 255.255.255.0
the gateway can remain blank

I have done the changes but now notice on startup of Linux i get a message that is too fast to read but failed is in RED and and it says something about failed to start network.

Before even trying to start LinucCNC you should verify that you can ping the FPGA card

Can you post the results of these commands:

/sbin/ifconfig

uname -a

ping 10.10.10.10

Attached is a PDF attachment listing the results as per your rquest

can you try just
ifconfig

Or if that doesnt work, try

ip a

alwyn@debian:~$ ifconfig
bash: ifconfig: command not found
alwyn@debian:~$ ip a
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1
link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
inet 127.0.0.1/8 scope host lo
valid_lft forever preferred_lft forever
inet6 ::1/128 scope host
valid_lft forever preferred_lft forever
2: enp1s0: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc pfifo_fast state DOWN group default qlen 1000
link/ether 1c:1b:0d:8e:36:25 brd ff:ff:ff:ff:ff:ff
alwyn@debian:~$

Looks like you do not have enp1s0 configured for a static ip address of 10.10.10.1 and it also appears unconnected

I am not very conversant with code so it would be greatly appreciated if you could supply the code necessary to connect the Ethernet. I would really like to get this system up and running as soon as possible.

This is a network setup issue, not really coding
I would suggest reading through:

wiki.debian.org/NetworkConfiguration

I have finally got Linux CNC configured to the MESA 7176E card and it it up and running.
There are however two other issues creating problems.
1). When I try use "gedit" nothing happens although it is listed in the ini. file. This tells me the app. was not iclude in the downloaded package, or need to be activated somehow.
If it was not included, is it possible to download it on a machine that has internet access and then transfer it to the Debian machine via USB.

The other question relates to "Axis". When I load the machine file created by using the config wizard, I get the followig error.
Error in -/.Axisrc
traceback (most recent call last)
File "/usr/bin/axis line 3513 in <module> execfile (rcfile)
File "/home/alwyn/.axis rc "line 3 in <module>
fullsize + maxgeo.split(' ')[03+'x' + maxgeo.split(' ')[1]
attributeError:('tuple' object has no attribute 'split'

There may be one or tw typo's in the above, but what does it relate to.
I am hoping you may be able to offer assistance in order to put this whole saga to rest.