Let’s assume that we didn’t have any knowledge of nuclear technology, and didn’t have the possibility of building nuclear power plants to generate electricity. That is, that we couldn’t use the current fission technology, and couldn’t look forward to developing fusion energy. We’ll assume that the best methods of large scale electric power generation were the “conventional” technologies that we have today: coal-, oil- or gas-fired boilers, gas turbine generators, diesel generators and the like, and hydro-electric generators.
In that case, we would be scrambling harder than we are to develop viable solar, wind, tidal and other forms of power production. Those things do work, after all, and can generate power. But let’s assume that even with our absent nuclear power options that development of those technologies had not improved beyond their present-day development and cost-per-kilowatt.
There would come a point where the incremental cost to obtain, refine and use the dregs of “exhausted” oil fields, deeper wells, farther offshore or in worse terrain would be higher than the cost of using the alternative technologies: wind, solar, tidal and more hydro. (We would certainly be damming a lot more rivers than we are!) At that point we would abandon the recovery effort to obtain that oil, coal and natural gas, and there would still be some in the ground.
I’m not going to make any specious claims about “magical new technology” that doesn’t yet exist, but the fact is that every second of every day the Sun puts out more energy than we even want to deal with. I’ve seen research on thunderstorms that show that every minute of every day there are some 1500 lightning strikes around the world and in the atmosphere. That’s a lot of untapped energy, too. As costs continue to rise to obtain the energy that we now use to maintain the status quo – and we never seem to be satisfied for long with the status quo, so our energy usage continues to increase – then more and more bright people are going to seek ways to tap some of the excess / unused energy that exists around us. The energy is demonstrably “there”; we just don’t know how to use it. (It’s even more plainly “there” than radiation is, since we can’t sense radiation except with instrumentation or by observing its secondary effects. Lightning strikes and heat from the Sun are plain to any observer.)
So, yes, I do think that we will discover and develop new sources of energy. The research these days into methanol production is particularly exciting. (Methanol can theoretically be generated from “any organic feedstock”, not necessarily the valuable crops such as corn, but perhaps corn stalks, grass clippings, leaves and tree bark, etc. – and coal itself.) If we don’t, then we’ll start damming those rivers, utilizing more solar and wind power – and being far more conservation-minded than we are, even to the point of living underground, perhaps. And having to be satisfied with the status quo, or shrinking our output of goods – and children.