There are several points to make about this:
Firstly, since this is an electronic device, and the old one had been working, presumably fine, why did it choose now to stop? Electronic devices of this type don’t tend to stop working unless there’s a good reason, so this may be more important than you might think.
Secondly, the chances of the old controlling system working directly with a new inverter, even from the same manufacturer, are not good. Chances are that the wiring will have to be modified to take account of the differences.
Thirdly, I’m a little concerned about the high/low speed switching arrangements. Is this a dual-winding motor? If it is, I have to say that they can be a complete nightmare when it comes to inverters. I’m aware of one installation where to get this to work at all without blowing up triacs on switching, zero-speed sensing and some extra logic had to be employed. The back emf generated in the winding not being used (especially when switching from high to low speed) can produce enough oomph to destroy even massively oversized and over-rated triacs.
I had a quick look at the manual for the new inverter, and it looks as though it follows a fairly typical layout, so the chances are that if it won’t start at all, you need first to be looking at the basic run diagram and where the links are. Then you need to look at the settings. And LADmachining is quite correct – just make sure initially that you have one winding (if there are two) connected permanently to the inverter output, or nothing will happen.
So initially, can you confirm exactly what sort of motor this is that you are using?