I'm guessing you have a DSL internet connection and you're experiencing what's called "sync, no surf" - the modem seems to be behaving properly, but you can't surf the internet.
It could be the modem - some modems that use the Alcatel chipsets were known to behave funny.
Or it's the phone line the modem is on which is behaving funny - there's too much interference on the line at times which causes the modem to hang.
Contact your ISP and ask them to test the parameters of the line, if the parameters meet the specification of whatever internet speed you have. The faster the internet connection, the better the line parameters must be to maintain a good connection.