In the sixties and seventies the computer technology simply did not exist to build de guidance systems and other sophisticated hardware required to go to the Moon.
It's true that computing technology of the time was really primitive compared to that of today, but a couple of things have to be considered.
NASA was at the cutting edge of technology, and if they didn't have it they could buy it. What they had available to them was well in advance of anything else around at the time. It doesn't take much computational power to plot a course to the Moon. We're talking Newtonian physics here that can be done on the back of an envelope by any experienced physicists. Unlike general-purpose computers, the Apollo guidance computer had to perform only one task: guidance. Most of the number crunching was performed at Mission Control on several mainframe computers. The results were then transmitted to the onboard computer, which acted upon them. The Apollo guidance computer was capable of computing only a small number of navigation problems itself. Since the guidance computer had to run only one program, that program could be put in ROM; thus, only a small amount of RAM was required to hold the temporary results of guidance calculations.
The hoax advocates tend to overrate the tasks performed by the onboard guidance computers of the 1960's. In fact, the Mercury spacecraft, 1961-63, flew into space without any onboard computer whatsoever, yet the trajectories were precisely controlled and the capsule was capable of fully automated control.
One of the most commonly quoted "facts" about technology from the sixties is that "a modern washing machine has more computational power than the first lander." This is a questionable fact, but it hardly matters. It's amazing what you can achieve with primitive computers if you're not worried about fancy user interfaces. Remember how much gaming power was contained in the mere 64 kilobytes of RAM of the computers of the early eighties? All the computing power needed for the interfaces of modern flight simulation programs is needed to generate the realistic graphic surroundings, not for the actual flying controls, which are mostly rather simple calculations. The Apollo missions didn't need to generate pretty surroundings on a screen.
