The Great Time Machine Hoax
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The Great Time Machine Hoax (1964) by Keith Laumer
SPOILER WARNING: Contains plot synopsis.
This novel begins with Chester W. Chester IV inheriting a run-down mansion and millions in back taxes. In order to pay the back taxes, he has decided to auction off the mansion and it's contents, including a massive computer (the Generalized Nonlinear Extrapolator, or "Genie".)
However, while examining the mansion and the computer with a friend, he hits on the idea of using the computer's capabilities (it demonstrates that it can solve complex problems involving historical fact and display realistic images of them) to create an elaborate hoax...a fake time machine.
He asks the computer to show him "real, three-D, big as life dinosaurs and plenty of em - and how about a four-wall presentation?"
The computer asks if it should employ a method of doing so that, "is a purely theoretical approach, which might prove simpler, if feasible, and would perhaps provide total verisimilitude..."
He tells the computer to "go to it." and the computer does. However, the computer has managed to ACTUALLY transport them through time, and on their second trip back, before they realise that they actually DO have a time machine, they make the mistake of leaving their arrival area, and become trapped in the past. Even when they manage to return to the present, their actions in the past have altered it completely, but they are able to use the computer to restore everything to the way it was.
