Here's what you should do:
1. Check the fuses: This is the most likely culprit. Your owner's manual will show you where the fuse box is located (usually under the dashboard or in the engine compartment). Pay particular attention to fuses related to the ignition system, the radio, and any that might be labeled "power," "accessory," or "ignition." Replace any blown fuses with fuses of the *same amperage rating*. Don't use a higher amperage fuse; that could cause further damage.
2. Check the battery: While unlikely to be directly caused by the short, the incident might have drained the battery significantly. Check the battery voltage with a multimeter. If it's low, charge it or jump-start the car.
3. Check the main power wires to the radio: Carefully inspect the wiring harness you connected to the radio. Make sure none of the wires are shorted or damaged. A short could have damaged the radio itself or another component in the car’s electrical system.
4. Inspect the wiring harness: If you have any suspicions that you may have pinched or damaged some wires during the installation (even unrelated to the radio), it's worth a thorough check. Look for any frayed or broken wires, especially those near where you worked.
5. Check for other blown fuses or damaged components: If checking the fuses and battery doesn't solve the problem, it's possible the short circuit damaged a more significant component, like a relay or control module. This is more complex and might require professional help from a mechanic or auto electrician. They have specialized diagnostic tools to identify the problem.
Important Considerations:
* Professional Help: If you're not comfortable working with car electronics, it's best to seek professional help. Incorrectly diagnosing and repairing electrical problems can lead to further damage or even injury.
* Do not attempt to jump start the vehicle if you suspect a significant short. This can lead to further damage to the electrical system.
The fact that the car won't start after a short circuit strongly points to an electrical problem caused by that short, not a separate mechanical issue. Start with the fuses and work your way through the steps above. If you are not comfortable doing any of this work yourself seek out professional help.