Dan,
No - and I apologize for making something very simple sound very complex.
May I try again?
We ground things to keep us from getting killed or the house burning down when something goes wrong with the machine.
If you hook up the ground wire from a three prong cord to the frame, you have taken a big step towards safety.
I live in a country which uses 230V for normal things like toasters and mixers and washers...so we tend to be a little cautious.
What I was - badly - explaining was the following:
Your washer has an electrical motor. A timer motor. A set of solinoids to let water in. Maybe a light, sorry, I don't remember. There is also the control panel.
A "perfect" grounding job would mean running a wire to each of these from one big grounding nut and bolt, where you have attached the ground wire from the three prong plug.
Sometimes, when you ground an older machine, the fuse blows immediately. This could be caused by any of the things I just listed - or a little thing called a capacitor or condenser. These "help" the motor run when it gets started. They wear out once they get past 30 or so (sort of like men) and often make the fuse blow. The solution is simple - have this little part replaced. They carry a big jolt of electricity - even unplugged - so you might want to have this done by an electrician.
I hope this helped. Sorry to be so confusing.