Hiya,
First off apologies for not replying sooner- in RL someone dropped dirty (flu) bomb on me and I've been AWOL for a couple of days.
I don't normally jump straight to assuming its always malware, but _Cynic_ is right to suggest you at least check the PC is clean. There's plenty of tools out there available and lots of threads on this forum that suggest good ones to try. (the hosts file should be scanned for nasties by these anyway.)
Given you have no access to the router yourself, someone must manage your connection to a degree, so if you are using a connection supplied by Work, or School residence etc- its possible some website access is blocked through a http proxy (whenever you visit websites these go via http) - However I would expect these to be blocked all the time, so I don't believe this relates to your query. If the laptop is on a wireless connection to the same router- this also confirms its not part of the issue, as both should be affected.
Having ensured the PC has not got some malware recently picked up, you can then also try to reset the TCP/IP Stack, which should set your connectivity to a clean state:
https://support.microsoft.com/en-us/kb/299357 (Follow the steps based on your own version of Windows.)
Going back to my last post if you find you still need to do this- the steps I requested were for the following reasons:
ipconfig /all (tells us everything about your NW adapter and its current settings)
netstat /aon (tells us about all current network connections and their current state - established, listening,wait etc)
tracert
www.cheese.com (should effectively provide a list of "stepping stones" taken from your router to the IP resolved in DNS for that website)
Essentially nothing personal is revealed by providing this info, apart from the actual IP address of your internet connection.
Lastly, don't forget to put your DNS setting back to automatic once all is ok. (revert the previous instructions provided by mrmuskrat)
Good Hunting!