On the fan-motors, dust and sometimes hair get caught around the motor-shaft. You can pull it out with tweezers, then re-lube the motor with household/3-in-one oil. (Gun-oil works great)
If you don't see any trapped-crud...just lube it.
That it starts out slow and then gets faster, could be what oil/lube is in there turned to goo...and as if lumbers-along, heats it up and it makes it thin enough to Sorta work.
Any fan thats blowing breakers, sounds about siezed-up...lube might yet fix it, worth a try. (Just don't over do it, just a drop or two on each end of the motor-shaft. (Front and back)
If you can't see the exposed-shaft on the back-side...look for a tiny hole or open crease, for oiling. Really old-style fans had Capped-oilers, lift a spring-loaded cap, drop oil in and release.
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