Is it possible to find on a market a simple 4.5V electric motor, that can be installed into LEGO Part 564c01?
The service pack No. 5000 is more and more difficult to find.
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First, check the assembly is correctly greased - they can throw a lot of sqeak out if they are needing a little grease even if the motor is fine!
I have looked in to this myself, but the cost and trouble just isn't worth it - you can buy a used working unit for around £8 to £12 from a used / vintage Lego parts site.
These motors are really good quality and almost last forever if looked after, so chances are you will get your £8 - £12 worth from a quality used one - regular off-the-shelf motors cost anywhere from £4 - £8 and that's if you can get a perfect size and voltage match not to mention getting the drive gear to fit it etc. Stick with buying a using original motor/full assembly and check it is suitably greased and looked after it
I have lots of Lego train sets and that was my answer to non-working motors. I look after them well, and they just keep going!