Hello everybody..!!
I want to connect Local Area Network(or Internet:I have Cable internet) manually after starting( or re-starting) my computer rather than windows automatically connects.
Is it possible to do this..?

Just disable the connection when you're not using it by going to "network connections" right click on the relevant connection, and select "disable". Then select "enable" when you want to use it again. If you don't want it to be enabled on start-up you'll have to be sure to disable it before you shut down the computer but this is probably your best option.

As an alternative, many firewall programs have an option to "lock down" the internet connection. It will depend on the program whether this will continue on reboot but it's an option to look into with your specific security software.

I don't want it to be enabled on startup and but i don't want to disable while turning off the computer..Is it possible..?

I don't know of a way inside windows to keep it from starting without having to disable it before shutting down. You can check with the settings of your firewall, it may let you lock-down by default and then open connection until restart.