Fossil fuels didn't pick up steam on Earth (pun intended) because of oil. Coal is plentiful and accessible in certain areas without complicated machinery. Wood and peat were also early fuel sources.
Coal all came to be during the Carboniferous era, between when trees evolved lignin, and bacteria evolved the ability to break it down. If you want to hamper the adoption of fossil fuels, imagine a world without a long Carboniferous era. Of course, that would be a very different world, with a lot more carbon in the atmosphere. It depends how much you want to handwave.
Perhaps the most accessible technology for capturing useful amounts of solar energy is capturing it as heat. You can actually store large amounts of heat energy from solar by heating liquid in solar collectors and pumping it through pipes into the ground. It turns out that heat doesn't migrate through the ground as fast as we usually think, and there's a lot of heat capacity in the ground. Most of the heat you pump down there will still be recoverable up to a year later. This means you can create stored geothermal energy from solar energy with relatively simple methods.
Geothermal can be used directly for heating buildings and even driving steam turbines. You could smelt ores (maybe?), make big machines and factories that way. You could run pumps for irrigation and pumping water out of mines, etc. 778
You could have an electricity grid once you invent generators. But you will not have portable power. The energy density is too low. Perhaps you could use compressed air motors for short range vehicles like we do now. Fossil fuels are very attractive for powering vehicles. And once you have steam engines, you'll have access to oil unless you handwave that away too.
Now there is one thing that blows the energy density of fossil fuels out of the water: nuclear fission. Solar thermal plus geothermal would get you access to uranium by mining. You could run centrifuges to refine it. Remember, the first nuclear bomb was created before computers were in widespread use. We understood enough about electricity to make generators before the internal combustion engine was huge. Plus, the first steam engines ran on wood.
So I think it's feasible to get where you're going if you somehow get rid of coal as an easy solution, get rid of oil as an easy solution, and accept that big ships, airships, etc., need to use nuclear.
Now methane... That's hard to ignore. Not sure what you'd do to handwave away methane. 479