Can Only Reach Google and YouTube, Other Sites Can Not Connect

Sorry for the typo above.  I meant to say "I have restarted the router/modem many many times"....

Sometimes a power cord yank is better than a restart -- use the BIG hammer.

Are you using an Xfinity gateway/modem?  If you are using Xfinity stuff, changing DNS on a client doesn't work now,  the gateway will hijack it back to Xfinity's DNS according to @EG .  You can still on 3rd party gear -- but I probably ought to check that with a pcap capture.  Perhaps they hijack that now too.

Maybe something else.  You said you were having some WiFi trouble.  WiFi trouble can also be due to connection trouble.  Are you stuck only getting to google/youtube/etc, if you use a hard wired Ethernet connection?  Maybe try the Ethernet port the next time it happens and see if it behaves the same.

Another thing to try.  What do the error logs and signal levels in your gateway look like?  Look at the "Check your Signal Levels" section, and check the logs too.   https://forums.xfinity.com/conversations/your-home-network/internet-troubleshooting-tips/602dae4ac5375f08cde52ea0

If the DHCP renew isn't working all the time, perhaps due to line conditions or mangled packets, or just unavailable DHCP servers, it could be a limbo state where ipv6 is working and ipv4 is not.  You might see errors in the gateway logs about that too, or a lot of DHCP fails/retries.

@flatlander3 Thank you so much for your reply, much appreciated.

We have a NetGear cable modem/router combo c6250.  I always just unplug the power cable and reconnect when I try to restart.  I am pretty sure it is using google DNS now, when I run nslookup, I can confirm the server used is 8.8.8.8

Interestingly, when the issue happens, nslookup command shows that all the domain names can be resolved, such as www.amazon.com, but browser cannot load the pages.  traderoute command shows it times out after going out to some comcast addresses, but the result is not consistent.  I don't think or I don't know how to interpret traceroute result, as I see request times out after some point even when things do work.  

So far, I cannot find any clues yet from either nslookup or traderoute tests.

I am going to try wired connection tonight to see if this is a WiFi specific issue, and check the logs and signal levels too.

Thank you very much.

@flatlander3 I did some test last night.  When the issue happened, using a wired ethernet connection on a windows laptop showed the same problem.  Youtube and google sites worked OK, but amazon.com and others did not.  I didn't get a chance to try ipconfig /flushdns.  I will try again tonight.  What is interesting is that this issue lasted two hours or so, from 8 to 10pm.  Then all worked fine.

At this point, does it sound like the issue is with Xfinity, outside of my modem/router?

I am new to this forum.  How to make this discussion visible to xfinity employee, such as XfinityMikeB or XfinityEthan?  It seems that I could not @ them directly.  Xfinity technical support on the phone is useless, all they did was asking me to reboot router multiple times and then told me everything looked fine on their end.

Thank you so much for your help.

Yep.  Line stats/line conditions are suspect, so look at the admin pages on your gateway.  Xfinity routing problem and Xfinity DHCP in your area are suspect.  On the first page on your Netgear where it shows "cable connection", on netgear that is usually where the line stats are at. Look for a bunch of uncorrectable errors and compare signal power/snr etc to the troubleshooting ink above.   Logs are usually at the "advanced  tab --> then Administration" link.

You obviously have at least an ipv6 or you wouldn't get anywhere.  There may also be a firmware bug, although Netgear does actually have a QA department, so, lower on the list. Your fail mode is not unique or a "one off", but it's usually a bad idea to rule out anything right down to the power cord while troubleshooting.

You might try connecting a phone to your wifi, but shut off cell service.  Same issue?  Another test.  Rules out your PC/Software with another OS/device.   Just cuts down on the potential failure matrix to a smaller list. 

How do you get @xfinity somethings?  Welp, tier one may send you a request here.  That's an up-sell opportunity for them, but then you may actually get help from tier 2 after that if you can escalate the problem.  It's a sad business plan, but that's how they do it.  No, a [Edited: "Inflammatory"] Xfinity gateway for $14/month won't fix it, neither will a "speed package upgrade" -- that will be tier 1's solution.

* Oh, I'd add -- is your Netgear physically "hot"?  I don't mean warm, I mean physically hot, uncomfortable, kind of worried about plastic melting hot?  Just another issue to take out of the fail matrix.