There is a cut scene from Terminator 1 (see video below at 3:31) indicating that Cyberdyne System existed prior to the first incident with the T-101.
The second film, however, indicates that Cyberdyne Systems investigated and exploited the technology they could salvage from the Terminator destroyed by Sarah Connor. Hence, I thought that Cyberdyne Systems was created to investigate remains of that first Terminator.
So, what exactly is their company history and how does the deleted scene (above) fit in?