Connection problems with brand new MacBook ...

About a week ago I set up my new 15" MacBook. It worked perfectly for a few hours then all of a sudden started telling me I was not connected to the internet. That said, the internet symbol at the top was clearly telling me that I was and that I was connected to my own network ... the only one I've had for many years. My desktop, iPhone printer and tv are having no issues at all and are connected to that network. I've spoken several times to Comcast and nothing has changed. Ever since this situation began this situation has continued, only now the pattern is that I can get online, things go okay, then within a few minutes I'm thrown offline. The internet symbol at the top ALWAYS contradicts this, showing that I am connected, and to my own network. I'm going crazy. Btw don't know if it's relevant but the two browsers I use are Safari and Firefox.