Christina,
You could play with transparency - if you get 4 very distinct, strong
colours (i.e. high saturation in the 'more colours...' selector) for your
initial circles, then take the transparency down to 50% or less (only
available on later versions of PPT) then you might get a distincive overlap.
I've had success with 2 and 3 circles this way, but if you have a 4-way
overlap in the middle then the base colours might not show through (maybe try
20-25% transparency).
Alternatively, if you don't have Illustrator/Photoshop, etc. you could try
making the circles unfilled and drawing a freeform shape at 400% view, then
filling it with a distinct colour - you could get close to a decent circle
this way - remember you can always edit the points of a freeform shape, and
the more points, the better the curve.