Aspirin helps (the person who's doing the cleaning).

You can call a professional to steam clean it - easy, fast, and $$$.

You can rent a steamer, not a lot of skill required but listen carefully to the how-to-use it. Not too many $$.

You can hire a strong adolescent to read the following instructions and provide the labor. Probably the least expensive, but hand labor is time-consuming and teens need frequent feeding. You can do it yourself, providing you are in flexible shape and don't strain your back or arm muscles.

Find the fuse (or mainbox switch) that protects the electricity and remove (or flip to off) to be sure there is no live current available to the fan; snicked fingers hurt.

This is one of the rare times I would consider using TSP, a high-strength cleaning powder/additive, usually available at the hardware store. It is not environmentally friendly and so should be used only in the most extreme case. 50 years of grease and dirt sound pretty extreme to me. But *before* purchasing/using TSP, try the other way:

Remove the mesh filters - if it has them. Pour boiling water through the mesh and then soak in hottest water that has 1/2 cup household ammonia added for each gallon. Let sit about an hour. Use a scrub brush to scrub the solution around the mesh. This will stink, so be sure the windows are wide open and use a portable fan to help move stinky air out the window.

In a glass bowl, make a solution of 1/4 cup ammonia +2 Tablespoon baking soda mixed into 1 quart very warm water. Using a plastic scrubbee, dip it in the solution and start scrubbing the fan blades and then the housing, about a handsized area at a time and work inwards towards yourself (so dirty water doesn't drip on cleaned area). Wipe the scrubbed area frequently with a clean dampened towel/rag/sock (I don't recommend using anything you'll want after this chore). The scrubbing will have to be repeated several times. Do NOT scrub any wires or electrical connections. Use a paper towel to wipe off the motor housing -- okay, use a bunch of towels, it will eventually come clean. Go outside and clean both sides of the flap and that side of the fan blades. Oil the flap hinges and where the blades join the body. If there is a stove hood, it will require the scrub and rinse process same as the housing and blades, however, *IF* it is stainless steel you can use 0000 steel wool (from hobby or hardware store) instead of the plastic scrubber. Rinse the steel pad often in clear water. Reassemble the unit including the rinsed filters. Turn on the electricity. Turn on the fan. If it works, pat yourself on the back. If it doesn't work, don't be surprised because there is a good chance the motor was burned out - or maybe just plain wore out. Buy a new fan unit (measure carefully, they come in several sizes) and either install it yourself or have an electrician install. Try to convince your mum that the hood and blades should be wiped off with an ammonia-window cleaner once a week so this doesn't happen again. Remind her that grease build-up has a very serious potential to cause fires, and it's easier and cheaper to remodel an un-burned kitchen.

I've only ever gone as far as cleaning mesh filters, but a lot of Oxy Clean and boiling water cleaned some filters in a rented apartment after soaking a half hour no scrubbing was required. I would have sworn these things were naturally brass colored - nope, they turned back to a silver color.

However, I would bet that the fan is simply dead. Many motors will continue to "hum" when you flip the switch and they are no longer able to turn.