Need help for internet connection

Ok this is the situation.

I'm currently using a Motorola Router (Model: SBG1000) connected to my iMac.

Internet connection can be done in both airport (wireless) and ethernet cable (direct connection).

when i connect both of them, the internet does not work. Safari failed to open the page though inside the network connections both are shown as connected.

I often have to restart the router and then run network diagnostics. Then my internet connection on my other PC running windows simultaneously drops the internet connection as a result of me restarting the router.

what is the issue here? can anyone help?

thanks.