A stem that was affected. Everything had died on it.

A leaf of my Zucchini plant.

Here is a zucchini that is affected as well.

to my eye.. the mold/mildew... is attacking otherwise dead material.... its part of the composting of such .....

its the 'effect' ...

now you need the 'cause' ... and i will have to leave that to others....

ken

You may find that borers are literally boring holes in the stem, inviting all manner of subsequent maladies as the plant dies.

Well most of my squash plant has died. I now understand why it's better to plant more than one! First time gardner here.

While I don't know what is causing this hairy substance, I found several clusters of tiny brown eggs on the underside of the squash and zucchini leaves. I saw what I originally thought was stink bugs, but now think is actually Squash Bugs. I wonder if that is what killed my plant. Still not sure what this white hairy stuff is though.

The whiteish fuzzy stuff may not have anything at all to do with what caused the problem although the Squash Bugs, or probably the Squash Vine Borer, is a better choice. That fuzz may be a fungus that is converting the now dead plant material into something the soil can put to use.
Talk with the people at your local office of the University of Delaware Cooperative Extension Service since they will have a better handle on particular plant problems in your area of the world.

Here is a link that might be useful: University of Delaware CES