Takes Long to Connect to the Internet

I have a computer running on 64bit Windows 7 Pro. I am having a number of problems with the internet connection. It takes long (about 15 seconds) to connect to the internet from sleep mode. The computer is connected to a Linksys switch, which is connected to a cable modem router. An exclamation mark indicating that there is no internet accessibility is displayed. I have tried changing the static address, disabling the firewall and malware option on the antivirus (Avast) that I am using, but still the problem persists. Please help.
Thanks.
