pass key 3, car will not start, hear relay click when key is in on or off positi

Many GM vehicles have a problem with the passkey/passlock system. Im not sure on the 2001 DeVille, but I would at least TRY this: turn the key into the ACC position (dont crank the car) and let it sit for 10 minutes. See if there is a THEFT light. after 10 minutes, try to start it. (this is how you reset the passlock system) This works on most GM's when the passkey system acts up, although I have not tried it with a DeVille. Good Luck.

I don't know about your 2001 De ville but, I had the same problem with my 95'. I called a mobile mechanic that I know of. He came out and measured the resistor in the key with a digital ohm meter and found another normal resistor of the same value. He then took the cover off the steering lower shaft. He soldered the resistor across the two wires coming from the switch to the computer. He told me to start my car. It started immediately and has ever since. For this I was charged $60. You may have to pay a bit more if you live further away than I do.(approximately 16 miles). I'll bet your security light is on.