Internet Issues

Starting about 2-3 days ago, my internet wouldnt stay connected, like I could reset my router and modem, and my laptop, and it would show im connected to the network, but it wouldnt allow me to access the Web, and if it did it would only be for the first few minutes, or in particular, til I tried to download something say a game. Then it would kick me off? Ive also recieved an error a handful of times saying that another computer on the network has the same IP as me. Ive done a system restore and restarted my modem and router, ive deleted the old connection and setup new, im not sure whats causing this? Please help!