Can't connect to internet but can ping SOME websites

Hello.
For the past few days, our home's internt is not connecting. However, when I ping google and tomshardware.com, it is responsive. I can also flush the dns and release/renew the ip address. I am at wits end! If anyone can help, I'd appreciate it. Also, our router is a linksys and the modem is an AT&T one. All the correct lights on our modem and router are on but the wireless connection is saying no internet access (@ both IPV6 & IPV4. I even tried the diagnostic tools of the network snd sharing center.

Have you tried temporarily disabling your firewall to rule it out? Also, at times an Internet suite (like norton) may be blocking. If you have one, try disabling it temporarily.

Have you tried rebooting your modem and router? Also, you may want to call your ISP and have them check the connections. A few years ago, it seemed like whenever it rained my connection would get spotty. It turns out that a connection at the pole was worn and lost some insulation. It wasn't a problem as long as it remainded dry. time-warner replace the connection and I've been fine since.

Call the ISP to rule that out as mentioned. I would disable IPv6 since you really don't need it in most cases.
After talking with the ISP, you may want to take your router out of the mix to see if it may be causing the issue. Also, within your router you should be able to verify the connection from the router to the ISP by IP address and a possible lease time. I would look there when you have the issue to make sure everything is correct. You should be able to release/renew at the router also.