Do you see the Roku boot screen on initial power up (the bouncing Roku logo)? Or does nothing ever appear? Have you tried a different HDMI port on the TV? Do you have a different TV to try it on? If you've tried all of this and it still doesn't give you the home page, then it sounds defective and I would exchange it for another device.
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To test further, try plugging your device into another TV. Go to Settings>Display type and manually select 720P. Then, plug the device back into your Toshiba TV and see if you are able to get display output.
As a last troubleshooting step, we'd also recommend trying a factory reset of your Streaming Stick.