Not knowing the specifics of that loco, I'd say that unless there is a detectable pattern that might lead you to a track location, you could have power pick-up issues. That narrows it (mostly
) to the loco - either dirty wheels, dirty/oxidized pick-ups (e.g. if the wipers rub the back of the wheels or axels), or bad wiring in the loco.
One other possibility is damaged siderods - they can cause a loco to stall seemingly at random, but more often at low speed when there is no momentum to "power through" the tight spot.
Anyway, to trouble shoot the electrical, the first thing is to see if the motor turns consistently when not engaged to the drivetrain. If it works while disconnected with power leads contacting the motor, then work your way "back to the track" to see if you can spot a weak link - e.g. bad wiring or oxidized connections/contact points.
If the tender does not have pick-ups, it can be fairly simple to add them. The most straightforward way is to use any electrical that is already there (e.g. some tenders are wired for lights, but not power pick-up). There are also kits that can be had.
Similarly for the drivetrain, see if it rolls with no (not minor, NO) hesitation smoothly and easily. Also check the quartering of the drivers before you take it apart. If this is not the problem, start further disassembly in logical steps (e.g. one piece at a time, one side at a time) until you remove a piece that lets it run freely. That should then be your trouble part. I would hope that Broadway could supply replacements if it is not fixable.
Your digital camera is your best friend here - take lots and lots of pictures so you'll have a guide to reassembly!
Hope that helps. I know it's frustrating to have an expensive display piece. Good luck restoring her to "active duty".
Andrew