Internet Connection Drops Constantly

Hello, I'm experiencing frequent problems with my Internet Connection. My
computer is connected to the Internet through a Motorola Surfboard modem from
Charter Communications. My computer will randomly disconnect from the
Internet around every hour. The modem still says that it is connected as will
my computer if I go to the Network and Sharing Center. Even though the
computer says that it is connected, no program can access the Internet.
Anytime I open a Firefox it will usually say "Cannot Find Server" and
Internet Explorer will just say that it cannot display the webpage. Sometimes
I will get popups from Windows (I believe, though it could be FireFox) trying
to connect to a broadband connection. It never works, though, and it asks for
a password and username. I do not have one, though. I have not set up any
sort of password for accessing any Internet connection on my computer. When I
first upgraded computers all I had to do was plug in the cable modem and
Vista automatically connected. It was perfect and I had no issues for quite a
while. The connection dropped on day and Charter walked me through a process
which reset my cable modem and got me back online. Ever since then I have
been having this issue where my computer randomly loses it's connection. I
was not able to get online for about an hour today. I did a System Restore to
see if anyone had possibly done something, but the problem presisted. I came
back later and now everything is running relatively fine!? It's like the
computer has a mind of it's own. Any help would be greatly appreciated. I
called Charter and it is supposedly normal for the connection to drop from
time to time. They suggest unplugging the modem for 30 seconds, but that does
nothing for my issue and their support pretty much ends there. Thanks.