There are a lot of people who don't agree when the first computer was built; in fact many say that the first actual conception of the idea of a computer was by J. H. Smith in 1782. He however never built the computer. His concept was called a difference engine.
   
Difference engines were put on the backburner until 1822, when Charles Babbage picked up the concept. He created a machine that used a decimal number system, and was powered by the cranking of a handle. Babbage was financed in his research by the British government, but they later would cut that support off. This did not stop Babbage though, he went on to design a more analytical machine, but later on he made it more improved and put out a difference engine #2, all this happened between 1834 and 1869. Babbage made leaps and bounds in his designs.
   
Still other people will argue that Babbage's machine was the first electronic computer. While an earlier concept was made called the Antikythera machine, which was a mechanic device that was used to calculate the position of astrological signs. This "earliest computer" was discovered on a shipwreck in the Mediterranean Sea, and it dates back to 250 BC. It's not known who designed this early device but it has been guessed to be designed by Archimedes, because it is similar to some of his other mechanical devices.
   
However, there are still other people who will argue that the abacus was truly the first computer. These were invented in China somewhere between 2600 BC and 300 BC. These abacus were used by clerks and merchants in China, they are felt to be the first computer by many people.
   
Alan Turing who was from Cambridge UK, he was drafted to the Bletchley park secret base where the work was being done on the WW3 enigma codes that the Germans were using. It was kept top secret until recently the name of this computer was Colossus; it was smashed into pieces at the end of the war.
   
The first known "modern computer" was invented during WWII, done by a German engineer named Konrad Zuse in 1941. This computer was named the Z3. It was an analog computer that was designed to stimulate the guidance system for rockets.
   
With some research it was found that Babbage did not build a complete machine. Thus it would be Zuse who invented the first electronic computer.
   
Thus to truly answer who invented the computer it’s not really simple. Really you have to say who all contributed to the make up of the computer. So many different people in history helped with these inventions, by their failures and successes.
   
So over all the first electronic computer was invented by John Vincent Ansoff. It was named the ABC, which stood for Anatasoff Berry Computer.
   
A lot of people would feel that IBM was the first in designing the PC, but really prior to them was the MITS Altair 8800, Apple II, TRS80, the Atari 800, and of course the Commodore 64. Still others say Altair was not first, but instead it was the Simon by Berkley Enterprises.
   
So as you can see who invented the first computer is like who did invent the registry cleaner, really up for grabs, and will be forever. But let's thank all these people who came up with an incredible machine that is hard to live our lives without.