Does the turbo look ok, no damage to the wheel or to the housing? How about the oil? Is it free of any debris? Those would be my first concerns. You would also want to check the intercooler for pooling oil. Could be a bad hose, leaking oil feed line or blown turbo seal in play.
As to why it won't start, check for any codes that might be set. Only critical issues set CELs, so don't go by that.
Test the battery for CCAs, voltage alone is not a good indicator of health.
Post pics of the battery and its' labels. Also of the engine bay without the appearance cover. Might be some clues that will trigger ideas for nonstart reasons