Okay, I was able to figure this one out by using:

=(COUNTIF(B:B,"7/1/09")*[new price])+(COUNTIF(B:B,"<7/1/09")*[old price])

However, I'm stumped at another portion of this spreadsheet which I didn't
mention, because it didn't occur to me right away.

Parallel to these dates in B I have names in A. They are repeating and so in
another section there is a table counting balances for each name. I can't
think of a way to implement this date-specific counting and multiplying
formula and take into account specific names.

The total should take into account that if Bob was served on 6/30/09 he was
charged, say, $1, but when Bob was served on 7/2/09, he was charged $2.

I'm totally stumped. Is this even possible?