The NTSB has revised the list of incidents that are subject to a report. The other requirements have remained the same. Details are here. Two changes affect Part 91 airplane operators. Reports must be made if a failure of the Electronic Flight Instruments occurs or and if a portion of a propeller is released while in flight.
The National Transportation Safety Board is an independent U.S. Federal agency that investigates every civil aviation accident in the United States and significant accidents in the other modes of transportation, conducts special investigations and safety studies, and issues safety recommendations to prevent future accidents. Safety Board investigators are on call 24 hours a day, 365 days a year. The reporting requirements for aviation are contained in NTSB §830.1. The original is split into a several pdf or text files that are difficult to read and are located here. The standard CFR version is located in Title 49 here.
Note that immediate notification of the NTSB is required for:
§830.5 Immediate notification.
(9) A complete loss of information, excluding flickering, from more than 50 percent of an aircraft’s cockpit displays known as:
(i) Electronic Flight Instrument System (EFIS) displays;
(ii) Engine Indication and Crew Alerting System (EICAS) displays;
(iii) Electronic Centralized Aircraft Monitor (ECAM) displays; or
(iv) Other displays of this type, which generally include a primary flight display (PFD), primary navigation display (PND), and other integrated displays;
Since this is an incident the following section applies.
§ 830.10 Preservation of aircraft wreckage, mail, cargo, and records.
(b) Prior to the time the Board or its authorized representative takes custody of aircraft wreckage, mail, or cargo, such wreckage, mail, or cargo may not be disturbed or moved…
It’s not clear what steps must be taken by the operator in this case. I suppose that since you are required to notify the NTSB immediately when there is a reportable event, they’ll tell you what to do with the airplane—e.g ground it, fly in VFR to your destination or home airport, etc.
Almost every FAA written test has questions relating to this section. It is not too long, so I’d recommend just studying it.