If you installed the radio, did you use the same power source that the previous radio used? It probably has a full time 12v (+) source for clock and preset memory, then a switched 12v (+) to turn on/off with the ignition.
One check you could try, usually newer radio models have all the wires for power and speakers incorporated in one multi terminal plug. Pull the plug on the back of the radio and try starting sequence. See if it still has the warning lights and buzzer. If you didn't install it and pulling the radio plug solves it, take it back to the shop that installed the radio. If you installed it, check that your power connections are the same as the old radio.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI