check for vacuum leak.
First you need to troubleshoot the 1994 LeSabre cruise control. Check the fuse, the cruise switch, the linkage, to find where the problem is. Check the vacuum lines on the engine as a vacuum leak can cause the cruise to not work properly.
We had the exact same thing happen on our 2003 ford escape. We took it to the repair shop and they discovered that the throttle cable from the actual cruise control unit inside the engine compartment had become disconnected from the throttle body. They put the cruise control's throttle cable back onto the throttle body and it worked just fine. No need to replace any parts, just labor to re-attach. Not sure how it came off, but since yours appears to have done the same; perhaps its just a design flaw. Thus, the cruise control is fully operational (which is why the light on your dash comes on when you engage the cruise control), but it has lost it's ability to actually apply throttle to the engine.
On top of the engine, drivers side.
It's on the passanger side in the engine compartment above the wheel. Follow the front throttle cable right to it.
if you have cruise try the gray/black wire coming from the cruise control module, in the engine compartment... it should be on the passenger side fire wall, it will also have a black cable going to the engine throttle body.
The cruise control relay is in the engine compartment on a 1994 Escort LX 1.9L. It is part of a bank of relay switches near the battery. The cruise control is also controlled by the electronic speed sensor on the throttle body (carburetor).
The throttle positioning sensor
It is located on the top of the engine, below the throttle. Get a light and look straight down between the two throttle cables "if it has cruise control". It is bolted down with one 12mm bolt.
The idle air controller is almost always located on the throttle body. You can find the throttle body by following the throttle cable to where it connects to the engine. There are some(very few) vehicles that have the IAC motor elsewhere on the intake manifold though.
right side center roundish looking with vacuum line and throttle cable
throttle position sensor believe it or not!
On my 1994 Mazda Navajo, which should be the same as an Explorer, their is a black plastic cover with 3 bolts on top of the engine. When you remove the cover the throttle and cruise control cables attach to the throttle lever there. My throttle is sticking but the problem seems to be where the cable attaches to the pedal.