This Java stuff is a red herring - you only need it for sites that use Java applets. It's not to be confused with JavaScript, which a lot of sites use - totally separate languages, despite the similar names. If you don't have Java, and you go to a site that uses it, the browser usually tells you to get it, but until then, it's not the problem.
Are you familiar with the concept of an IP Address? It's the first thing to check when a connection is iffy, and you do it like this:
- open a command line window (start / run / type "cmd")
- type the following command on the command line: ipconfig
- do this when the connection appears to be up, and when it's down, and compare them.
- if it returns "0.0.0.0" for the IP Address at any time, your internet connection won't work. If that happens, you need to talk to your internet provider and see what they say. I don't know anything about your connection, whether you have a "router" or not, so I don't know whether the problem is at the ISP, or in the box they gave you,