The 3600 Streaming Stick "should" work with your TV. Perhaps try replacing the power adapter (use a cell phone USB charging adapter 5volt 1amp).
Am assuming your older Roku device worked in this HDMI port, and I am really not seeing any settings other than picture settings that may contribute to the issue. Try going into your picture settings and selecting either Theater Wide2 or Full picture size. (available when in 720p mode)
Your TV supports resolutions "up to 1080i" so the Roku 3600 will have to use 720p since not compatible/does not support 480i/480p. As such, need to make sure the HDMI is configured to recognize 720p.
If this Roku 3600 has been manually set to use 1080p on another TV, you may need to take it to another TV and manually set it to 720p in order for it to recognize your Toshiba. Settings/System/Display Type/720p (manually assign, do not use auto detect). Otherwise, maybe try Factory Resetting the Roku 3600 (press and hold reset button for 30+seconds) and hopefully the Roku will automatically detect the 720p capability of the tv. Just make sure you have a working Roku remote paired with this 3600 before doing this.
I would try seeing if the 3600 works on another TV first before factory reset, but if this is not an option, may be your best shot. I am thinking the 3600 is either not recognizing the 720p capability (stuck in 1080p mode or bad HDMI cable) or the power supply (adapter) may be bad. Those would be the first things I would check/swap.
Roku Community Streaming Expert
Just another Roku user... I am not a Roku employee.
Insignia RokuTV, Ultra 4660x, Premiere+ 3921, Express 4k+ 3941