Will not start after new stereo installed

How did you install the new unit? Many vehicles use the factory stereo for more than just sound. In this case it does not appear to be used for anything other than sound. However, your no-start is because the instrument panel is out. It contains the circuitry for the key recognition system, if it does not power up you will not be able to start the engine.

I would probably start by unplugging the new stereo and putting the old one back in, then see if the dash comes back. It is possible the new unit is sending out a signal or is wired in a way that it shuts off the dash.
The first thing the dealer will do is see the aftermarket unit and tell you it is the problem, so you might as well find out now if it is (happens a lot on vehicles newer that around 2000).