Navigate to this below path and reset all zones to default and check if the issue gets fixed.

Tools>Internet Options - Security tab, click "Reset all zones to default"...

Also you need to add the blocked sites to trusted zone and check for the issue.
 
To do so follow the below steps.

-Click Tools and Internet Options
-Click the Security tab, trusted sites and click the Sites button
-Uncheck the box underneath the website list indicating "Require server verification ..."
-Type the wesite name in the box and click Add
-Click Close
-Click the Privacy tab and the Settings button under Pop-up Blocker
-Add website to the list

Also check if your Anti-virus program or a third-party Addon is blocking cookies.

the issue may be caused due to a corrupted add-on in Internet Explorer. To confirm the same, run Internet Explorer in no add-ons mode and check if the issue persists.

To open Internet Explorer in no add-ons mode, 

Click the Start button, click All Programs, click Accessories, click System Tools, and then click Internet Explorer (No Add-ons).

If disabling all add-ons solves the problem, you might want to use Add-on Manager to disable all add-ons and then turn on add-ons only as you need them. This will allow you to figure out which add-on is causing the problem.

Delete the corrupted add-on and restart Internet Explorer normally and check if the issue reappears.