Here is a write up I did for Humidifier fan motors---
the same principle applies to pedestal fans, too-- You are right-- the bearings get dried out-- and the shaft 'STICKS!!
Let me know what you tihink of this write up-- try it and let me now what I left out-

Mack B

Have you considered checking to see if the fan motor might just need cleaning and lubricating?
Most small fans and heaters, have small fan motors, in which the bearings have dried out over the years. If you have made an electrical check on the motor leads-- and you have electric going into the windings, likely the motor feels warm? (If not-- possibly a bad splice where the supply wire attaches to the tiny armature wires?-- check , and check continuity)

If you want to tear into the fan motor, and clean up and lubricate the bearings-- here are some tips:

First you need to get inside the heater of the fan housing-- by removing the protective covers.
Note the screws, sizes, locations, and how the protective covers will go back on when you are ready to reassembly-- Mark where the screw holes are that line up with the matching other parts.

Then remove the motor from it's bracket (Possibly have to remove the fan first?)
You will have to remove the fan, to lubricate both front and real bearings.
Next you will need to remove the 4 long screws that hold the motor frame together-- Be sure to mark the original alignment, so you can reassembly correctly.

Now, with the fan removed, gently separate the Front and rear half's of the motor. Usually the windings will stay with the portion of the motor where the wires are still attached. Either way, you are going to have to get the bearings to slide off both Shafts of the armature-- without breaking the delicate winding wires-- the wires are hair thin on small motors!

Now clean up the caked on residue on the shaft where the bearings ride, with rubbing alcohol. Clean up the internals of the bearings as best you can- making sure the pores of the oil-lite bearings are not plugged with solids. Now begin the gentle process of getting the bearing wicking to soak up new oil. When you are sure the reservoirs are well saturated, then generously lubricate the shafts, and slip them thru the bearings again-- retracing all your steps above, The motor shaft should turn freely now. You can test the motor without the fan on-- to be sure you have the motor itself reassembled properly.

Double check all the splices, switches, and any high temperature limit switches for continuity-- and trace the wiring all the way back out thru the power supply cord.

What did you find, and what do you need to do next?