Any network or Internet experts out there? Help needed.

I am having this weird problems with our internet at work. Once or twice a day (and virtually every night) the internet goes down. Basically the internet light goes out on the 2wire modem and the browser tells us that it can't connect to service provider. At that point you can either restart the modem from within the browser or unplug and power cycle which usually fixes the problem. The unusual part is, we have somebody that often works from home and she is still able to connect to her computer here at the office even if the internet is down. One night I verified this and was able to log on to my computer here, but when I opened a browser it said it couldn't connect to the service provider. Another unusual instance was one time when the internet went down during the day I had several browser windows open and every time I would click on something it would tell the can't connect to the service provider message, except for one window (oddly enough, clutchfans) I was able to click on new topics and pages I hadn't visited and it would still open up. Anyway, we've changed the modem 3 times and they all do the same thing. We've had three different people come out from AT&T and they can't seem to figure anything out (they seem fixated that it is the modem). When it goes down I've run some diagnostics and it says "Unable to contact the Domain Name Server"

Any help or suggestion would be helpful. I think we are going to try AT&T out again today this afternoon (or maybe not till Wednesday) so if any you any thoughts on what the problem might be to help maybe point them in the right direction again would be super helpful.

Thanks in advance.

More info:
Modem 2Wire 2700
No routers, but we have 2 switches behind the modem.
We have a static IP address and have had it for a long time something AT&T calls a "legacy static IP"

Again thanks. And if you have any other question feel free to ask.

 

Thanks guys.

I have updated the Primary DNS to the google DNS and everything seems fine. Should I change the secondary to something else? Does google have a second DNS or do I need to use an OpenDNS?

I won't know if it is fixed until either it goes back down sometime today or tomorrow (if it is still up, in the morning).

Reviewing what the DNS does. I guess that would explain why we can connect to the computers remotely but not browse the internet. Am I correct?

Though, the one time clutchfans was still working still confuses me.

Again thanks.

 

Check that, of course I looked up Google DNS (which I should have done before posting the other message) and they do have a second DNS (8.8.4.4) and will update the secondary to that unless for some reason, you'll think otherwise.

Again thanks.

 

Just wanted to let everyone know that as of today, Wednesday, everything has run smoothly.

Thanks to everybody (especially FrancisFan).