The fact that it is happening on more than one computer does suggest a networking problem.
The biggest question left unanswered in this post is if the laptops are connecting wirelessly? If they are, bingo, you found your problem.
Try hard wiring a laptop for the time being to test.
If the connection is intermittent, you may appear to have successful pings, but they may be sporadic with jittery response times, or intermittent dropped packets. It may also appear that some sites load occasionally, while others fail. I'm not entirely convinced that all your HTTPS sites are working, and that ping is always working. Can you verify that by trying an extended ping test. Use the -t parameter to perform a continuous ping test over a period of several minutes. Watch for lost packets and uneven response times.
However, if they are wireless as I first mentioned, you need to focus on that, it is almost certainly your problem. Multiple wireless access points, interference, problematic firmware, etc. can cause network issues such as you mention.