Ok I have had a similar problem with my '92 park ave and found one problem and got it to finally work. Look by the battery on the fender well and look for the ground cable from the engine block to there. I had mine melt down on me while driving. The engine ground and body ground connect through there. This if in a high resistance state will cause all sorts of weird electrical problems to show up.

I am pretty sure that I took this connection apart and sanded the surfaces and lubed them with grease a few weeks ago when my problem was an intermittent problem and it did not make any difference.
I agree that my problem appears to be, from my experience with cars in general, some kind of connection issue. The low hanging fruit has been checked and now it is more of a concerted check of what part of the car is actually not working. I believe that I have eliminated the Crankshaft Position sensor and the Ignition Control Module as problem sources.

Alright now that I see the rest of your posts, The buzzing rattle that you talk about has me thinking about the fuse and relay panel up under the passenger kick panel. There is the fuel pump relay there and some other items in there for drivability. Check those, Pull and reseat. I only know about this due to a friend having some of the same problems when his fuel pump would stop working. There is also the connector in the back of the car for the fuel pump itself. His for some reason had loose contacts inside that connector. Also while you have those relays out, check to see if you have any resistance between battery negative and the relay point. I just had this morning my ground on the ICM go high resistance on me. Bypassed with a wire directly to the bat negative.

Good idea. I am going to do what you suggest after I check the signal from the Ig.Control Module to the ECM/PCM. I also want to reseat and clean the connectors to the ECM/PCM. I have not got to it yet as my better half has me doing her honeydew list..... Hopefully this afternoon.....
By the way I read one thread where someone had trouble with the ground on the Ig Cntrl. Module turns out GM relied on the case of the ICM for ground and it didn't always work out. The fix is a ground wire to the case of the ICM. GM put one there later I think the 92 was one that didn't have it. I was not sure where the relay for the fuel pump was located. My Chilton'* manual really sucks leaving out really important information.

CDA Joe: I forgot to add that the ground wire should go to the ground pin on ICM and then it is a solid connection.
BTW I grew up in Pullman, WA and spent lots of time there over the years. Still own my parents house there. We drive usually and several times in the now dead Buick maybe 10 times in the last 5 years. Nice to take I-90 out there and then 95 down the Idaho side. Coeur d' Alene is really nice. We are located just a couple of miles from the eastern end of I-90 In Boston also known as the Massachusetts Turnpike.

Fuel Pump relay is pictured on the kick panel. If you have the remote door lock module there is also a relay there for the trunk release. Not a common option on the Lesabre though. Could get the module out of the wrecking yard of the Park Ave same year. And yes I did put a wire in from the ground wire to the Engine block ground when I saw the high resistance.

If you feel frogy enough you could use a wire from B+ to the terminal listed in the schematic for turning on the fuel pump. This will tell you if the fuel pump is working. Or you could swipe one of the others for temp to see if that helps with the running condition.


Here is a rough idea of what the relay center looks like under the passenger kick panel.

CDAJoe:
Thanks for all of the assistance and the schematic.
Got an inconsistent result when testing the fuel control line on the ICM. Nothing was present with ignition on and engine not cranking. When the engine was cranking on one attempt I thought I could see a varying low voltage no more than a 2 volts though the DVM was on DC voltage and it might have been AC. Then I could not detect anything. I am not sure what that voltage should be. I think I will try your ideas now.

OK just looked at AllData Schematic of the fuel pump relay. If you connect connections 87 and 30, you might have to look at the bottom of the relay for a good picture of the connections, you should hear your fuel pump turn on when the ignition is in the pre-start position. If you want to see if power shows up when you crank the engine, connect red lead from DVM to contact 30 and black to known ground. This will tell you if your oil pressure switch is allowing the pump to turn on.

This may have to wait until tomorrow. Is this Alldata online or is it something to purchase?