To be more specific, if I am on a certain date and then click a time I would
expect to get a form to fill in with that date and time already filled in for
the start time.

When you click on the day view of the calendar and then click on the time link,
it should auto-populate the day and time for you:

Yeah, you'd think it would work like that but it doesn't. Does it work for you?
If so I guess there is a setting I need to change.

Ah, I see the problem. I created a custom list with a calendar view! If I add
the date fields from the "Event" content type it automagically picks up the
selected date and time. Sweet!

Yes it does auto-populate, what you have is probably a scripting issue.

Can you try it from someone else's computer or from a different type of
browser to see if it works? If it does, then it's a problem with your
browser, if it doesn't, there is a problem with the server script files, have
these been customized?

I was trying to do this with a custom list, and a calendar view. It works fine
when it is based off of a real calendar.