If you are changing the IP address of your computer within the LAN, then I don't think this will have any problem with the internet connection, as it's just a local address, problems arise with the internet if you try to change the IP address of the network card that is getting the main internet connection. If you are having a DSL modem, this one has an IP address, if you change this, don't expect the internet to work anymore
Bare in mind that this case is only valid with DSL connections with fixed IP address in which your DSL modem has a fixed IP address assigned to it by the ISP. If not, you will find that there is no IP address assigned to the DSL as far as I know.