And I wonder if a private owner could even manage to start the engine without a team of mechanics and their equipment. I think I read once that F1 teams have to hook the engines up to devices that pre-heat the oil and coolant before starting them, since the engines don't want to run (or can't run) when cold.
Depends on how you want to define cost.
You could probably buy a roller (no drivetrain) 'show car' for half a million or so. But that's a far cry from what it cost McLaren.
That car is one of seven chassis built for the 2006 World Championship season, the first of the now-defunct V8 engine formula. It is estimated that McLaren's budget for that year was $406.5 million. (Which would actually be closer to $600 million if Mercedes' expenditures on the powerplant were factored in) Of that, maybe 30%-35% can be directly attributable to designing, building and testing the car. Divide that by seven, and you get ~$17 million per car.
Ferrari operates the F1 Clienti
program under their Corsa Clienti banner. Basically, you pay about $1 million and you get an ex-F1 car (at least two years removed from competition, which I think is to adhere to FIA testing restrictions) and a team of mechanics who bring the vehicles to certain tracks around the world and give you the keys. (Maintenance costs are a tightly held secret, but it's rumored to be around $1 million per anum.) The most popular cars are from the early 2000s; full on traction control and much more forgiving aerodynamics make them comparatively easy to drive. But you want Reubens Barrichello's F2002? Right you go. Gerhard Berger's 412T2 from 1995? Sure. Gilles Villeneuve's 312T5 from 1980? Might take some time to fabricate spares, but okay. But I would recommend you stay away from the F399 challenger from 1999..... they had some..... 'issues'......
If I had been about ten years younger (and single) when the program launched, I think I would have tried to volunteer as a marshal.
Seriously, you want to have a laugh, go to YouTube and search "Ferrari F1 Clienti" then select the video of your choice, sit back and watch the hamburgers tool about Laguna Seca or Miller Motorsports Park.