Why my internet acts strangely?

I am having a reliance broadband connection( wired ) .But recently my internet started acting strangely.Lyk,mozilla wont load google.com,but chrome can,chrome cannot load certain pages but mozilla can........etc...also my connection drops of in between and my computer says it is not connected to net,but all my modem lights are working ok,and there is no problem wid modem.Is it the problem wid ISP,or my computer or something else??PLSSSSS help