Imagine a world that has no oil, coal or natural gas. It probably would be identical to ours until the start of the industrial revolution.
The steam engine is created, but requires wood in abundance. Massive deforestation follows. After that, industrialization only takes off in the deltas of large rivers where huge quantities of logs could be transported by water. The steamships stay mostly at Mark Twain's levels and do not venture into open seas. Very slow development of railroads ensues. Ethanol engines appear by the end of the 19th century, but they are inefficient, and ethanol is expensive.
Electricity is discovered at about the same time as in OTL, but, other than in telegraphy, it stays a parlor trick for a while. City lighting does not progress beyond candles and oil lamps. However, major investments are soon directed towards harnessing wind and water power. In a curious twist, industry shifts to the areas with better access to electricity, which includes many mountainous regions (eg, see
US wind power map). Some of the electricity is used to produce hydrogen for
fertilizers which leads to additional population disbalances. As a result, the disparity between more and less developed regions is very pronounced for a long time.
There are no world wars, no densely settled cities, no significant working class, so the pace of changes never reaches our levels. However, various local conflicts flare up. Scotland breaks free together with Liverpool, as well as the Basque County and Galicia. Switzerland becomes a kernel of the Alpine Confederation that includes Northern Italy, Southern France and Bavaria, but the rest of Germany is still fragmented. Other small countries with new access to power experience rapid development: Iceland and Norway, as well as Japan (much later, though, as Commodore Perry never arrives).
Colonialism does not even begin to decline until the end of the 20th century. China is partitioned between European powers, and the Emperor's court rules only over Szechuan and Tibet that are doing rather well.
United States (minus the Confederate Part) experiences wrenching realignment as the New England and Great Lakes region lose the competition with the newly rich Mountain states. Chief Seattle manages to play off against each other US and British Empire and establishes a de facto Indian State that eventually expands into British Columbia, Oregon and Washington State. The 1906 San Francisco earthquake interrupts the Gold Rush, so California develops very slowly much outside of the mountainous regions.
90% of world's helium
is in the US, so American air companies dominate the market, though smaller competitors with hydrogen airships constantly try to undercut them. It's a tough business, as hydrogen zeppelins are very expensive to insure.
Electricity storage and transmission is another hot investment area, and regional electrical grids develop around mid-20th century. This leads to military needle-thin airships with tops speeds reaching 150 mph and air-refueling capabilities (ie, battery exchange). Air defense, however, still can easily pick them off, so super-heavy artillery and dreadnoughts remain weapons of choice. Only later hybrid electric-ethanol engines and crude ballistic missiles begin to challenge the usual calculations.
Nuclear energy is glimpsed at by the and of 20th century, but due to the lack of experience with building power plants it takes decades to arrive at relatively safe plant designs. Even later, first nuclear ships begin to take off. Nuclear weapons are banned outright.
In about 400 years, this world's history converges with ours...
(As you can guess, I don't have much knowledge of energy technologies, but I would like very much to see what more experienced readers can contribute. )