Integrated Motor Assist (IMA) battery failures are not uncommon. The IMA battery will require replacement when it fails.
2004 Honda Insight Problem Reports
Most Reported 2004 Honda Insight Problem Reports
The automatic transmission (CVT) can have a "shudder" due to a worn start clutch. Replacing the start clutch should correct this type of shudder condition.
A binding gas cap can cause the Check Engine Light to illuminate. Replacing the filler neck is needed for this repair.