Internet Connection Issue with MacBook Pro 2010 model

I've begun living in an apartment in Germany, and the service provider is a company called Unity Media. The internet connection behaves in a very strange way. It takes a long time for the Mac (OS X 10.6.8) to recognize that there's a cable/wifi connection. When it does, I have about two minutes during which I can open new tabs in Chrome and access information. After that, I can't open new tabs. That is, I can open them, but I get a "This Website is Not Available" error message. What's also puzzling is that my gmail tab (always open) remains functional. I think this might have something to do with the computer itself because my iPad/cell phone both are able to connect to the modem's wireless signal and function more or less normally. Does anyone have similar experiences/solutions? Thanks.