Why won't my capacitors work?
When you crank a stepper motor, it generates AC.  Your capacitors look like a short circuit to AC, so all the current flows through the capacitor and none through the LED. This is also the reason it gets hard to crank. The short circuit allows a lot of current to flow.  You have to crank hard to generate the high current.
At a closer look, both of your linked motors are stepper motors.  Both will generate AC when cranked.
You have three options:

Leave out the capacitor, and use two LEDs in anti-parallel.  The LEDs will flash, but when one is on the other will be off.  This protects the LEDs (somewhat) from the extremes of reverse voltage from the AC.
Put a rectifier diode in series with the LED, and the capacitor in parallel with the LED only.  That gets DC for the LED, which the capacitor can smooth.
Get a DC motor, and use your LED with the capacitor in parallel.  You'll have try cranking the motor in both directions to see which will make the LED light up.

Regardless of which solution you choose, keep in mind that you have to crank the motor fast to reach its rated voltage.  If the motor is rated 5V at 3000 RPM, then you will have to &quot;crank it&quot; at 3000 RPM to get 5V out of it.