The proper name for the "Check Engine" light, might actually be a "Check Emissions" light. Short of an engine stall, it only activates when there's a problem that causes abnormal tailpipe emissions.
This means that your computer is likely storing codes, and not triggering that light. It may be more convenient to have the local parts store connect an OBD-II code reader to it, and read those stored codes. Since it's new, the dealer should also do it for free. Some dealers may not necessarily be forthcoming with certain information for fear of you demanding an expensive repair, a different vehicle or dropping the loan.
If interested, there are options for buying cheap bluetooth OBD-II hardware, coupled with cheap or free OBD-II reading software for PC and phone. OBD-II diagnostic software also exists but can be expensive.