Could he technically start a new country? XD
Edit: Oh, right.
If that's a practical question, then all he has to do is to declare independence and then be prepared to win a war against the United States when it chooses to militarily dispute that claim. As Larry Ellison is unlikely to be able to win a war against the United States, I'd say the answer here is also no.
The practical process for starting a country is to control a piece of land militarily, declare yourself independent, and then persuade other countries to recognize your claim. They're incredibly unlikely to do so, unless you can really back that claim up with something. Even countries which are large, have functioning governments and reasonably powerful militaries can't be guaranteed universal acceptance, e.g. Taiwan.
Nobody will sell you land on which to start your own country. Your best bet for land not currently subject to any territorial claims would be Marie Byrd Land:
http://en.wikipedia.org/wiki/Marie_Byrd_Land
a Mongolia-sized slice of unclaimed land in Antarctica. You'd still have a tough time getting anyone to accept your claim, though. Also, it's cold.
Well, there is no global legal process for starting a country because pretty much all territory is already claimed.
However, plenty of countries have split apart recently (e.g. Czechoslovakia into the Czech Republic and Slovakia) and indeed by own "country" of Scotland is about to consider splitting from the UK.
The most clear example of this is the Statute of Westminster 1931, which the Parliament of the UK passed in order to create a legal process by which its colonies could file for legal independence.
As I understand it, in British law classes, there is often a question asked of students: "If Parliament repealed the Statute of Westminster today, would we (in principle, legally) get all of those colonies back? Does Parliament have the right to repeal the Statute of Westminster and the grants of independence under it, or were they something otherwise unprecedented in law: a surrender, effective forever, of certain legal powers?" Etc.
So yes, there are sometimes legal processes for starting a country, although the U.S. doesn't really have one. The U.S. does allow you to apply for statehood however, so it might be interesting to immediately declare independence (illegally) and then immediately apply to become a state (legally) to see which imperative wins out.
If you'd rule fairly, you even could have a chance of Western world accepting you, as even good dictatorship would be a massive improvement compared to the current conditions.
I wonder… "Hey Operations? It's Larry. Shut down all Oracle and Java applications running inside .gov networks. Right now. Every single one."
;-)
If he builds a monorail, I guess it'll be obvious.