John:
Welcome.
Typically, these things (lgb) run, almost forever.
There are many possibilities, but id suggest simply taking it to a train store for repair. Im guessing that you need a new motor, about 60£.
Add service time. Another 60£ ill guess, for example, clean, grease removal and replacement.
Obviously, i have no real idea.
You have whats called a clamshell gearbox, ie to sides to create the gear box. No problems, per se, but do require a lot more work to disassemble and reassemble. Also, you motor will have a tiny ball bearing in the gear box, at each end of the motor shaft. These must not be lost if you use the old motor.
Do the wheels turn, and do the gear/rods move freely?
Your loco looks to be in good condition and modest wear.
Does the headlight light when power is applied(try both directions).
Train repair can be costly. You might be able to find another, used, in your price range. Or, this could lead from pan to fire.
As mentioned, your locos do not have independent control.
You can run both on the same track. They may or may not run at the same speed. or, as mentioned, set up a separate loop, eg, an inner and outer loop, connected by points. Or something rather more clever….
Something you CAN do, is to carefully turn the loco over, protecting whistles and bells, and take the leads from your transformer and touch them, simultaneously, to the different sides of the loco wheel sets. Sometimes, the pick up brushes that touch the back of the wheels dont make full contact. These do wear out and are designed to be replaced. Trying the direct lead can cause the wheels to shift side to side and complete an otherwise faulty contact. Wont hurt to try. Then, you may determine, or not, if the motor is faulty.
Best of luck.