so, what keeps the military from killing the president and other govt leaders now?
corporations are practically governments themselves. they have similar authority structures. i would imagine the corporation would print its own banknotes, or would trade in some item that has intrinsic value. in the past many places printed their own banknotes and they were accepted in various other places for trade. and they would likely accept them in the company owned stores.
people would work for the militia because they would indeed be paid and the force of the militia would provide backing for the companies own banknotes, similar to how you seem to think the govt somehow magically provides value to their currency.
yes indeed i think a 70 year old suit is going to maintain control. money buys loyalty and i guarantee the business men are smart and would be paying their militia well. what makes you think they wouldn't be able to find something of value to continue paying them? they are big and already control a lot of resources. those resources can be converted into something to pay the employees and keep them loyal. they would just hire a few more employees to maintain security.
in the power vacuum if the government suddenly disappeared, large corporations are the best suited to take their place as they already have the internal control and authority structures setup.