Wow, that is a relic of a washing machine. But, it is a Whirlpool, so no wonder it is still around. My Whirlpool dish washer is 30 years old and still working like a charm!!
The model/serial number is located somewhere on every appliance. The typical places to find that information is to look behind the washing machine for a plate or sticker, check under the lid itself or on the area surrounding the tub drum.
There are replacement appliance parts available on-line. I just bought replacement knobs, burners and a blower for my 30 year old Jen-Air oven range by doing a simple google search which lead me to a parts supplier. Once you find the model number, you too can search the internet for the parts you need.