I was wondering if you were going to bring up Ada Lovelace (after whom the Ada computer language was named).
I don't think one can really credit Ada as inventing the computer, although she is credited with possibly being the first computer programmer.
Whether Babbage, or Turing, or who, invented the computer rather depends on what you are defining to be a computer.
The French would argue that Pascal invented the computer, and some might even argue that the Chinese abacus was the first computer - but then these were not what we would now regard as programmable
computers (actually, the term 'computer
' initially was applied to people who computed, rather than computing machines.
The modern idea of a computer as a stored program machine did not come into being until 1948 (several designs were experimentally implemented by several groups in 1948 and 1949).http://en.wikipedia.org/wiki/Turing_complete
Charles Babbage's analytical engine (1830s) would have been the first Turing-complete machine if it had ever been built, but the first actual implementation appeared in 1941: the program-controlled Z3 of Konrad Zuse. The universality of the Z3 was shown by Raúl Rojas in 1998. Prior to Rojas' 1998 paper, the first machine known to be Turing-complete was ENIAC (1946).