Answer: This is truly a job for Sherlock Holmes! Let's try to get to the bottom of this...
It is not unusual for various insects to visit a pumpkin bloom. Generally, they pose little threat. It is also not unusual for the blooms to close halfway through the day.
My opinion is that your lack of pumkins is due to a pollination problem. Make sure you have both male and female (have a mini pumpkin below the flower) blooms. Sometimes it takes time for the plant to produce both - male blooms appear first, and the female blooms follow. Check also to see if bees are busy on the flowers. Insecticides can kill them and leave you with their job!
Try pollinating a few blooms by hand using an artists paintbrush to transfer pollen from a male to a female blossom. This may help.
It is conceivable that pests are destroying the reproductive structures in the flower before the fruit is fertilized. A remedy for this would be to treat the culprit, but I would be very concerned about harm to the bees. If you see that the caterpillars are eating the center of the flower, try some Bacillus thuringiensis, known as B.t. (sold in many brand names). It won't hurt the bees. If there are small yellow and black striped beetles among the horde, they can be repelled with oil of cloves. Just soak whole or powdered cloves in oil, and dab the strong-scented product on cotton balls. Position these near the blooms, and the beetles should stay away. If these ideas serve to keep most, but not all of the pests away, you'll need to have the other critters identified so you can find an effective repellent or control. I know that neem seed extract is a broad-spectrum repellent, and may serve to keep ALL your pests at bay! You'll find neem-based products in the Gardens Alive catalog (5100 Schenley Pl., Lawrenceburg IN 47025; ph# 812/537-8650). Good luck!
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