1994 Buick Le Sabre starts first time, runs great. Won't restart until something has cooled off.

When you turn the key on the fuel pump should pump for about five to ten seconds. Do this a few times and it should start. Even with a full tank the pump will do this to pressurize the system. If the pump keeps running it's not picking up fuel. Have a friend listen at the gas cap with the cap removed for the pump to cycle. If it doesn't work there is a fitting on the fuel rail that looks like a valve on a tire. Take the cap off of it and use a small screwdriver to push the center in and see if there is pressure in the fuel rail. Have the key on and wear safety glasses.You should get a squirt of fuel out of it. If you have no pressure there the pump could be bad or the filter plugged. If there is pressure you have other problems. There is no shut off switch. Only fuses and a fuel pump relay. https://www.google.com/search?client=ms-android-samsung&source=android-browser&ei=_skGWP71NoOFmwGwvp-YCw&q=1998+buick+lesabre+fuel+pump+switch+location&oq=+1998+Buick+le+sabre+fuel+pump+switch+location&gs_l=mobile-gws-serp.1.0.30i10k1.20246.66235.0.71699.52.41.2.0.0.0.354.6560.4j26j8j2.40.0....0...1.1.64.mobile-gws-serp..17.35.5853...0i10k1j0i7i10i30k1j0i13k1j33i21k1j33i160k1.pAvwOOuWlKU#imgrc=99du9RTFFGCYhM%3A&scso=uid_WAbKSQAIdFcKJtQCGQCAqw_8:0

If it is a 3.8 engine change the crank sensor,they go bad on the 3.8 engines.

NO POWER TO FUEL PUMP......CHECK ALL IN LINE WIRING
NOT FIRING... START WITH COIL PACK, DIST CAP ETC...PLUGS/WIRES??????
"HOT WIRE" (DIRECT W/ FUSED JUMPER) TO FUEL .PUMP....NO - GO,,,BAD PUMP

Check your idle air control valve and/or egr valve, assuming that its cranking over and not running, if not the starter can be old and getting to much heat off the exhaust.

try changing the plug wires

Have you checked fuel pressure? How about spark on all 6 cylinders? Maybe a coil?

There is shraider valve on the fuel rail to test pressure, it can also be used to releive fuel pressure.
There is no need to dissable the fuel pump and crank the engine.

I had the same problem with my 2000 le sabre custom. It would die in the middle of the interstate. I could throw it into neutral and it would restart and keep on going or I'd have to let it sit for about 5 minutes and it would usually start. There is no code, Dealer said to bring it in when it's happening. Yeah, right..if it's drivable..it's not happening. Replaced the fuel pump twice, the camshaft and crankshaft sensors, but still happened randomly. I had to stop driving the car because it was unsafe.

its the electrical connection at he fuel pump,if this is ok ask if they replaced the strainer on your fuel pump,your fuel pump is inside your gas tank ,you have to drop the tank to service,most fuel pumps are not warrantied if you dont change the strainer,when your car shuts off the sediment on the strainer falls back into the tank,but when you run your car and it sucks up the gas thru the strainer to the pump it clogs the strainer and the fuel pump cant pump,you shoiuld find out if they changed this because your forcing your fuel pump to work harder,was it a new fuel tank or used one that they put in