yum commands produce "No module named sqlite" error

Issue

• When trying to use yum, we see the following error:

# yum install gcc
There was a problem importing one of the Python modules
required to run yum. The error leading to this problem was:

   No module named sqlite

Please install a package which provides this module, or
verify that the module is installed correctly.

It's possible that the above module doesn't match the
current version of Python, which is:
2.6.6 (r266:84292, Nov 21 2013, 10:50:32)
[GCC 4.4.7 20120313 (Red Hat 4.4.7-4)]

If you cannot solve this problem yourself, please go to
the yum faq at:
  http://yum.baseurl.org/wiki/Faq

• When trying to list rpms installed with the rpm command, nothing returned.
• trying to install packages via rpm also fails, ie:

# rpm -ivh sqlite-3.6.20-1.el6_7.2.x86_64.rpm
error: sqlite-3.6.20-1.el6_7.2.x86_64.rpm: Header V3 RSA/SHA256 Signature, key ID fd431d51: BAD
error: sqlite-3.6.20-1.el6_7.2.x86_64.rpm cannot be installed

• The rpm command fails with error as below,

# rpm -qa
error: Failed to initialize NSS library