2 Computer Sharing Same Internet

Well first let me get started by saying that I use a wireless router (linksys) that is connected to a comcast modem. Well the modem hooks up to the wireless router then the main computer receives internet through a Ethernet cable that is run from the linksys router to my main computer. Well whenever I turn on my laptop I temporary get disconnected from the internet on my main computer for about 3 seconds, it shows the internet still connected but I get disconnected from my internet services such as online games/vent. I'm not sure how to disable this from happening, Its very annoying getting disconnected like this. Anyone know what to do?