When you turn your key to the START position the idiot lights turn on for a few seconds so you can do a light check.
They should stay on as long as the key is in the "Start" position. If your car has an automatic transmission, put the shifter in gear and turn the key to the start position. The Oil, Temp, and Brake (and maybe seat belt) lights should light up, and not go out until you release from the start position...
Well either the bulbs are burnt out or there is a bad connection (or no connection). Are your Oil and Temp sending units hooked up? 'Might be time to pull out the instrument cluster and have a look at things...
Possibly the "prove out" circuit in ignition switch has failed. It's only purpose is power the warning lights when starting to confirm bulbs are working. The oil pressure light should illuminate with switch on, engine not started. If not, the oil pressure sender has likely failed. Can ground it's connector to test bulb circuit.