How far back do you mean by old days? Computers can date back to BC. For example the Abacus, was considered a computer. 
"An abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes."
"The abacus - the first known calculator, was probably invented by the Babylonians as an aid to simple arithmetic around this date. This laid the foundations for positional notation and later computing developments."
However, it wasn't until the 1800s or so that computers started to be more like machines that could mechanically perform a task for what they were built for.
In 1822: "Charles Babbage designed his first mechanical computer, the first prototype of the decimal difference engine for tabulating polynomials."
It wasn't until about the 1900s in which computers were used for communication. But it wasn't until 1970 that computers started to look more like what we know as computers nowadays:
"The Xerox Alto (picture shown) was an early personal computer developed at Xerox PARC in 1973. It was the first computer to use the desktop metaphor and graphical user interface (GUI).
It was not a commercial product, but several thousand units were built and were heavily used at PARC and at several universities for many years. The Alto greatly influenced the design of personal computers in the following decades, notably the Macintosh and the first Sun workstations. It is now very rare and is a valuable collector's item."
|Includes CC-BY-SA content from Wikipedia's Abacus article (authors)|
|Includes CC-BY-SA content from Wikipedia's Timeline_of_computing_2400_BC–1949 article (authors)|
|Includes CC-BY-SA content from Wikipedia's Xerox_Alto article (authors)|