Unable to solve apt-get issues Ubuntu 14.04

Question

I am using Ubuntu 14.04. When I was using a wifi connection everything was working fine. Recently I have switched to a wired connection. From then when I try to update and install packages through command line, I am facing problems. When I sudo apt-get update, at the end of the output it is showing

Fetched 3,506 kB in 4min 48s (12.1 kB/s)                                       
W: GPG error: http://archive.canonical.com trusty Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <[e-mail]>
W: Failed to fetch http://in.archive.ubuntu.com/ubuntu/dists/trusty/Release  Unable to find expected entry 'restricted/source/Sources' in Release file (Wrong sources.list entry or malformed file)

E: Some index files failed to download. They have been ignored, or old ones used instead.

And also when I try to install packages, for example r-base-core, it is showing unmet dependencies

Reading package lists... Done
Building dependency tree       
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 r-base-core : Depends: libblas3 but it is not installable or
                        libblas.so.3 but it is not installable
               Depends: liblapack3 but it is not installable or
                        liblapack.so.3 but it is not installable
               Recommends: r-recommended but it is not going to be installed
               Recommends: r-base-dev but it is not going to be installed
               Recommends: r-doc-html but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

I have tried all of the following solutions but still the problem persists. I do not want to reinstall Ubuntu, many other softwares were installed in it.

solution1, solution2, solution3, solution4.

Any help will be greatly appreciated.