Replaced ignition lock barrel on my 2000 mitsubishi eclipse. Now it will turn over, dash lights are on, but it won't start

You say 'ignition lock barrel'. Do you mean ignition/steering lock cylinder? With a new key, too?

Read this:
Your vehicle is equipped with an immobilizer system consisting of the ignition key, the key ring antenna, the immobilizer-ECU, and the ECM or PCM . The ignition key, has a built-in transponder. The key ring antenna is installed on the steering lock key cylinder. Only the registered ignition key permits the engine to start, therefore, the engine can never be started by means of a forged key or by connecting the ignition wiring directly or non-registered replacement key(s). The system is significantly safe and reliable against theft. In addition, the driver has only to turn the ignition switch to the "ON " position to activate the immobilizer system. If the requirements for starting the engine are not satisfied, the engine will be immobilized. If the ignition key is lost or another ignition key is added, the encrypted code can be registered or erased by using scan tool MB991502, available at your local dealership, or in some cases, a mobile lock service can perform the registration on-site. Call around to local locksmiths to see if they can be of assistance.

To add to the Captain's post:
http://www.socalevo.net/gallery/albums/userpics/10201/rke.pdf