It appears from your diagram that the Computer and NAS are on the same local area network connected through two ethernet ports on your router.
What make/model router do you have? Do you know if the ethernet ports on the router are a hub or a switch? Traffic between your computer and NAS shouldn't affect the bandwidth of the other devices, unless everything was connected together on a hub.
Are the ports on the router 100mbit or 1000mbit? If your router only has 100mbit ports, then upgrading to a 1000mbit switch would certainly increase performance between devices, as long as your devices support 1000mbit connections.
Also, I would check your network cabling between all your devices to make sure they are at least Cat5e if you're connecting at 1000mbit. I don't know for sure, but inadequate cable ratings may add additional crosstalk and interference between network ports.
It's a D-LINK DIR-655 like many people have here. It's still the best reliable one around. I got mine in 2008 or something and today, they are still selling it in the market. I have already updated to 1.35FW NA which is the latest. All Right now, I have all ethernet ports connected to my router including my VoIP modem, AV HomePlug, etc.