There was also a fourth factor, the concentration of a literate and mechanically skilled[1] workforce in the areas that industrialised first, the Midlands.

Making ploughs and other agricultural machinery, cutlery, military arms, and other bits of machinery (axles for carts and carriages for instance).

The exploitation of coal for kinetic energy allowed the industrial revolution to continue, but yes, it certainly got underway well before coal had any contribution of this sort.

I would add that because nearly all of it is invisible, the role of heat in industrial processes is now widely underestimated. Making salt, the precursor for many chemicals as well as having many uses itself; scouring wool, making bricks (way more efficient than using stone), and many more. Coal enabled all of these to be scaled up well beyond the carrying capacity of any country's forests.

Edit: oh, and of course iron smelting!

1. But not particularly well paid.