Internet Access Randomly Drops On Wired & Wireless Connection?

I've got an older Acer Timeline 4810t running Windows 7. We recently switched from Cox Cable internet to AT&T U-Verse, and I've started noticing that my internet connection will randomly go out when I am connected. This occurs whether I am on a wired or wireless connection. Specifically, I will be browsing the web and, randomly, when I try to pull up a website, I get an error indicating that I cannot connect to that website because I am not connected to the internet. When I check the status of my connection in the bottom right corner, it will show that I am connected to the internet. If I disconnect the ethernet cable (or disconnect and reconnect to the wifi network), the internet service is restored, although it continues to randomly lose connection.

I initially thought that it was a U-Verse issue, so AT&T came out and replaced the router. Unfortunately, I still got the random drops. I then thought it was a Windows issue, so I reformatted by hard drive and reinstalled Windows - still having that issue.My wife has an older Macbook and does not have this problem. We also do not have this problem with any of the tablets or phones that connect to the network wirelessly.I am beyond frustrated and do not know what to do. I also don't know if this is a sign that my laptop is at the end of its life, which would be unfortunate since I've only owned the laptop for about 3 years (my last laptop, a Dell, is on year 7 and still churning).