If the motor has brushes and it has an ac rating on its nameplate, it is a "universal" motor- it will run on ac or dc. Assuming that the "motor integrity is OK", make sure that it is operating at rated volyage, in your case 230 volts, (And not 110 volts). If the motor is only getting 110 volts to run, it will likely operate as you describe. Make sure that the brushes are not worn down too much also- but you rewinder probably checked that.
I have found with small room fans, the real problem is eventually the bearings- which are just plain sleeve bearings, get dirty and sticky, and the motor becomes "stuck" in the bearings. This is why fans usually start on the fastest setting.