A film of sticky residue leftover from old oil can create enough friction to prevent starting, particularly if a small motor has been over-oiled in the past.
Some old oils, such as 3-in-1, that will eventually dry out from even moderate heat, leave a very sticky residue, and small motors can appear to be fine when spun by hand, but the motor may still be unable to start reliably.
The bearings and shafts need to be washed thoroughly with a solvent that's capable of cutting thru the waxy residue. I generally use lacquer thinner, although a naptha solvent will most likely work well (wax & grease remover, cigarrette lighter fluid, etc). Stoddard solvent (aka WD40) will likely work, too.
A quick squirt of pushbutton-miracle-in-a-can won't do a good job. The motor may start fine that day, but likely be very unreliable in the near future.
To do a complete cleaning job, it's better to remove the rotor and briskly rub the bearing holes and rotor shaft areas with swabs or similar applicator.. I use white cleaning materials so it's easier to see when the yellow waxy residue has been removed.
If the motor has wool felt-type material in the bearing lubricators, they should be soaked and wicked-out with dry paper towels or cloth (saturate the wick then press a highly absorbant material against the wick to draw out the nasty old residue). Otherwise, the old waxy crud in the wicks will contaminate any new oil that's added. Some motors have a foam-like material for the oilers, and that material is likely to crumble and fall out.
I've found out that the old waxy residue in wicks will make the new oil sticky, and have had to then perform the saturate-and-wick-out of the old crud, then reassemble the motor.
After a complete cleanout of the old oil, the small motors I've cleaned have had enough torque to be able to spin up a fan blade or small centrifugal blower wheels.. and continue to operate reliably.