On a whim, I visited Wiki and looked up its list of the defining technological advancements of the Industrial Revolution. I'll summarize what might have happened to that list from the perspective of coal not being present.
Generally, without hydrocarbons, the industrial revolution would have been delayed and the global power brokers might be different. But, ultimately, it would have happened anyway. There's nothing you can do with coal, oil, or natural gas that can't be done with something else.
Please bear in mind that at the same time the Industrial Revolution took place, so did substantial advancements in chemistry and electricity — including Faraday's discovery of electrical generation. By itself, wind- and water-based electrical generation combined with the use of motors would have replaced most of the industrial revoution's advancements. (I don't count solar electrical generation as solar panels weren't invented intil the 1950's. Even with scientific pressure from the loss of hydrocarbons, it's unlikely — impossible IMHO — that they would play any roll in an industrial revolution.)
The technologies that would be most impacted by the loss of hydrocarbons are (a) those depending on heat (especially those that require a lot of heat over a large area) and (b) those depending on transportation.
Concerning (a): Electricity is great for creating a lot of heat in a small area and mediocre for greating a little heat in a large area, but it's lousy (at least back then) for big-heat-big-area problems. However, solar could replace big-heat-big-area fossil fuel solutions, making cloudy days very inconvenient, but it could be done. Non-hydrocarbon chemical reaction could also do it, and chemistry was a big part of the Industrial Revolution.
Concerning (b): transportation would be the most delayed aspect of development, waiting until either a chemical process, improved battery technology, or electrical distribution could replace the combustion engine.
My conclusion, if you don't want to read through my list, is that the Industrial Revolution would have occured anyway, but it may have been 30-60 years late. Even hydrocarbon lubricants can be replaced by non-hydrocarbon solutions. Necessity being the mother of invention, the increased demands of population and industry would simply have sought solutions elsewhere. You can always overestimate humanity's collective wisdom — but you should never underestimate its collective genius.
Politically, the revolution would have basically occured among the same nations. The focus might have shifted to Germany rather than remaining in England (mountainous waterfalls would be an advantage); but, ultimately, it I believe it would still have been something born in Europe.
Here's the list of technologies that defined the Industrial Revolution.
enhanced by automation. That automation was already well underway due to mater-driven mechanization. Easily attained with electrical replacements.
Metallurgy: is more difficult to achieve with electricity, but not impossible. It's a big-heat/small-area problem. Add to this solar heating or non-hydrocarbon chemical processes and most if not all of the value of fossil fuels can be replaced.
Steam power: suffers greatly as does the transportation that is powered by it. Machines that depend on a fixed-location motor can be driven by electricity. But mobile engines like trains won't come to pass for a long time (see Transportation (Railroad), below). However, somebody would be thinking about how to do this almost instantly. Once a more-powerful-than-my-horse motor (chemically or electrically powered) comes into existence, inventors across the world would be looking for ways to make it mobile.
Machine tools: Like textiles, would suffer almost not at all as they are as easily driven by electric motors as by steam.
Chemicals: This important aspect of the Industrial Revolution would be impacted little by the loss of fossil fuels. In fact, the development of chemicals and chemical processes might actually have been enhanced by their lack. Chemical batteries would have been very high on the list of developments. Also high on the list would be chemical reactions that could produce any form of motive force. Chemistry, alone, may have replaced fossil fuels; it simply would have required more time.
Cement: Not impacted by the lack of fossil fuels other than due to transportation.
Gas lighting: Wouldn't exist, but would be quickly replaced by arc lighting followed by filament lighting.
Glass making: Would be affected moderately due to the heating problem identified above. If solar heating couldn't fix this problem then it might have been overcome by converting the original sheet glass process to one that could use high-heat/small-area solutions.
Paper machine: Probably unaffected other than transportation. This remarkably important contribution to the Industrial Revolution would still happen.
The British Agricultural Revolution is considered one of the causes of the Industrial Revolution because improved agricultural productivity freed up workers to work in other sectors of the economy. And the British Agricultural Revolution had nothing to do with fossil fuels. It would have been unaffected and its value toward the Industrial Revolution in general untarnished.
Mining: While electricity might have replaced steam engines, delaying but ultimately not affecting the mines' contribution to the industrial revolution, the fact that one of England's biggest mining operations at the time was coal means the focus of value would have shifted elsewhere.
Other developments included more efficient water wheels, based on experiments conducted by the British engineer John Smeaton the beginnings of a machine industry and the rediscovery of concrete (based on hydraulic lime mortar) by John Smeaton, which had been lost for 1300 years. Neither of which would have been effected by the loss of fossil fuels.
Transportation (Canals): It's the building of canals that would be slowed for the lack of steam-powered tools, but they would eventually be replaced by electric tools. The value of the canals would remain intact.
Transportation (Roads): Again, the building of roads would be slowed, but the value of roads would remain intact — although their ultimate value would not be realized until either battery technology or chemically-induced motive power could replace steam and, later, gasoline.
Transportation (Railways): This is the big one. Steam could move mountains. It could eventually be replaced by electricity, but only after an energy storage system or energy distribution system could replace combustion engines.