Sounds like its had a good run.
That being said I don't know how long the NOW sticks are meant to last with consistent use. Have you considered purchasing another Roku stick or Amazon fire stick?
Update - took it over to neighbour. Their TV is a ROKU TV and is 2 years old. Stick came up fine with app screen.
Back to my errant Toshiba and no change - still splash screen and then black. Tried changing the Pic Mode using Toshiba remote and discovered that the Pic Mode menu doesn't display over the Now stick Black screen.
I suspect that this will end with purchase of a new TV - Mrs. Nowandthen2 will not be happy if she can't watch Tour de France on Channel 4!
Thank you to everyone who has replied.
If you don't want to fork out a lot of money for a replacement television then maybe consider an alternative NOW supported playback device.
Do you know anybody who has an Amazon Fire Stick for example you can temporary borrow to test out on your Toshiba television ?
I doubt this has any bearing, but i would try both 2.4ghz and 5ghz wifi frequencies on the Stick (even if the Stick worked on another television in a different room in your home) should your Router be dual band.
Whilst trying both wifi frequency bands on your Router (assuming you have a dual band Router) with the NOW Stick, also try unplugging the Router at the power outlet for about 2 minutes if you haven't done it already.
if you do manage to borrow another NOW Supported playback device to hook up with your Toshiba television that is not a NOW Stick, then make sure after use you log out completely on the NOW App with your sign in details under the My Account tile box at the bottom of the NOW App home screen page.