Car won't start after radio install

Just in case this isn’t a PASSLOCK problem, I’ll add one thing to my comment about fuses.
You state that you did not cut any wires; only connected to wires that were already cut. Fair enough.

The point there is that connecting a radio lead to one of those already cut wires could create a short and pop a fuse. Maybe a power antenna lead as an example and to which I might add the following.
Some years ago a customer bought a brand new VW and balked at the price on a stereo upgrade at the dealer where I worked. Two weeks later it was towed in for a no-start and the entire wire harness behind the dash was fried; all because of a power antenna lead that he kept attaching to ground. Just sayin’…