the dash lights come on appears to be normal but no starter turn over. Cross jumped the solenoid and would start but not stay running.
car will only start if you cross jump the solenoid on 1991 Buick Riviera
Start by checking the fuses and fuse links after that you would need a wiring diagram to check for power to and out of the ignition switch. There is a company that independent auto repair shops get their information from, this same information is available inexpensively for people that work on their own cars.. The information is year make and model specific, covering repair procedures, torque specifications, fluid capacities and specifications, service bulletins, component locations, wiring diagrams ect.... Alldata is very easy to navigate http://bit.ly/AllData_Repair_Manuals_Online