I was under the impression that the squash vine borer damaged the vine itself (ie. the stems and leaf stalks), so the leaves would be affected, not the fruit. I've never had SVB but apparently they can easily be found around the base of the plant, where they will be making holes in the stems.

Your problem does not sound like an insect pest, possibly some disease (viral or fungal maybe) or nutrient deficiency.

I am going to chime in. Your squash are not being pollinated are are dropping from the plant. This is normal. If the squash are pollinated they develop otherwise they will stop producing. Definitely not squash vine borer as it kills the entire plant. Try and pollinate the flowers when they are open and see if this helps the squash develop.