Jim and Bob - thanks much for the thoughts and advice.  I'll try checking the engine later this week and report back.

Further info, for what it's worth:  the Mountaineer set box describes the engine as a "Bachmann Plus GP35 Locomotive with operating headlight"; it is blue with Conrail markings and the number 2324.  Is there any diagnostic that can be done to determine whether its motor is just not working anymore, and that this would be the problem?

Jim and Bob - thanks for the help.  Jim - your setup is exactly how I had it when I described the problem I was having.  I'm thinking that it may be that, as Bob suggests, the engine is the problem after all.  I'll see if I can find out what model it is and post again later. If it helps, it is the standard engine that came with the Mountaineer set, and yes, it has been in storage for a couple years.

Tried as you suggested, but no luck.  Plus, with that configuration, two red cables going from the DC screws on the power pack to both sides of the straight track piece, I don't have a red cable to go from the AC screws to the turnout controller accessories (which I know I had connected when the system ran properly a couple years ago when it was last set up).

My son was given a used E-Z Track "Mountaineer" set, which came with the Spectrum Magnum power pack.  The set-up also includes two turn-out controllers.  I've made the cable connections the way I think they're supposed to be, and the controllers work, but the train does not run.  Please, if anyone can tell me what I've done wrong, I'd appreciate it.  Here's how it's wired up now:  one red cable from the "Variable DC" points on the power pack to the track; the other red cable from the "Accessories AC" points on the power pack to the turnout controller switches.  The turnout controllers operate correctly, and when the speed dial is turned up, the lights in the train engine gradually brighten, but it does not move.  Any help would be appreciated.