The rail lines exist, and they're based on government largesse a century ago.
From what I understand, they are not suitable for high speed trains.
The government just needs to grow a pair and stop subsidizing the current losers who are running the the rail into the ground (similar to the car companies, the banks, the airlines) and offer it out.
You mean like the government owned corporation Amtrak?
What other infrastructure investment is needed. The company that builds the thing pays for everything - that's part of the deal.
Well then I highly doubt that would work. No company is going to spend that kind of money on a project that is sure to lose money. The prices would have to be exorbitant to cover costs. Amtrak tickets are often more expensive than plane tickets and they still lose money. And this new company would still have to make back a huge initial investment.