To answer your questions:
I downloaded Toshiba’s H.D.D. Protection software and it won't run in wine (wine tricks disappears)left the menu bar tab to the left.
WINE is just a compatibility layer so all it does is simulate Windows features. What you want is to get low level information WINE does not have a clue about. Status of hardware you always need to check with the running OS.
How do I know if its running? or how do i get it to run?
You will not get this Windows software to run. Never ever.
Now for the good news...
"Toshiba’s H.D.D. Protection software" does nothing but read out SMART data and that comes standard with Linux (so Ubuntu too) in the form of
Anything else it claims to be is marketing: there is no software that can react as fast as hardware. Example: the hardware detects that the heads are going to crash microseconds before it does. By the time the software is told it is going to happen it already happened. So all the software can do is predict on past events when the drive might fail.
But companies like to install "disk protection software" and advertise it, because people (mostly Windows users ;) ) think it will be helpful and buy it.
Some topics about SMART (that include commands to see SMART data):
By the way: for SMART to work you need a modern hard disc (though I doubt anyone is using one that does not have SMART).