First of all, it's not a CDI. It's a Digital Igniter. Whats the difference? One is a microcomputer (Similar to the spark control box in your car), the other isn't.
If your battery exploded, I'd be grabbing a continuity tester and running down the wiring harness. Have you checked your fuses and relays yet? There is an ignition relay right next to the battery, if it's not working then the DI and the rest of the bike won't get proper power. Yeah, it's possible that the Digital Igniter is bad, but I'd think you'd have seen smoke with that kind of pop.
If it is bad, you are going to be fighting an uphill battle to find a new one. There are some posts that detail how to possibly fix them, it depends on whats blown.
Before we start buying stuff to replace ('cause it's expensive), we should be trying to figure out whats bad. Check the simple stuff first. Check the operation of all the switchs, don't forget about the sidestand ignition cutoff switch as well. Best done with a cheap $10 radioshack continuity tester