Annoying 3-speed fan issue after replacing capacitor

I’ve just replaced the capacitor on my 3-speed floor-standing fan, and while it starts and runs fine on speed 1, if you try and start it on speeds 2 or 3 it acts like the capacitor’s bad, i.e. you can hear the motor but the blades barely move and you have to spin them by hand to get them working.

If you start it on speed 1, you can then switch to speeds 2 or 3 with no problems.

Any ideas as to why it’s behaving like this?

Sure, an obvious workaround it always to start it on speed 1, but before the old capacitor started failing you could start it on any speed and it worked normally.