Answer:
The engine runs while starting because the spark plugs are getting electricity from the battery via the ignition coil and distributor. When the key leaves the start position to go back to the normal "run" position, the spark plugs must get their energy from the alternator. I would start with the alternator (probably the most common part to go bad), you can test it or remove it and take it to Advance Auto or one of the parts places and they can test it. If it is bad then replace, else put it back on. If your problem isn't fixed at this point then you will want to have it towed to a shop or buy a 68 Cutlass/442 shop manual from Ebay or fusick.com (if you want to learn how to fix this yourself). The next steps are a little more involved, checking the voltage regulator, alternator circuit, ignition switch etc. If it just started doing this one day, and you didnt do anything to it ;), then its probably 80-90% likely to be a bad alternator.
Its position will no longer be the same.
Probably the starter, have someone turn the key to the crank position while you gently tap the starter with a hammer or bar. If it starts change the starter. If not try shorting the starter solenoid to see if that works.
Is the selenoid getting power when the switch is turned to the start position? If yes, it's not a switch problem. Is power coming THROUGH the switch and to the starter when the key is turned to start? If not, it's a selenoid problem. If yes, it's a starter problem.
My Chevy was doing the same thing. It turned out that the connectionc on the starter were getting wet and arching. check that the ceramic shiled is fully intact AND THAT THE WIRES AND CONNECTIONS ARE SECURE TO THE STARTER.
your ignition switch is hanging up in the crank position.
It is probably caused by the ignition switch internals shifting (I had a similar problem before) and it turned out to be the ignition switch)
Most starters have two mounting bolts and one thick wire (usually around 10mm or more) which goes to the starter relay and from there to the "+" side of the battery.The starter circuit is completed through the starter's mounting bolts - which are screwed onto the engine - and from there to the "-" side of the battery.Depending on the vehicle make and model, the starter relay is activated when the ignition key is turned to the "Start" position or when a separate "Start button" is pressed.
Besides the smart alec answer "start an automobile", a starter has a small gear, that will both extend as well as rotate when the key is turned. This gear will engage teeth on the flywheel/flexplate, which is bolted to the rear of the crankshaft. As the starter turns, the engine will be turned.
A 1986 Ford F150 starter won't stuff off when the key is turned off if the ignition switch is jammed. This will cause the start signal to be sent to the starter continuously.
Let's leave it with being an anti-theft device or other mark of possession that activates electrical systems, and on many cars will activate the starter when turned to the extreme clockwise position.
Could be the ignition switch, the starter, a faulty wire, the battery...
The starter relay feeds power to the starter when the switch is turned to start. The relay will be mounted either on the fender or on the firewall.