Where can I find some reliable statistics about the prevalance of equity in private companies during the 80's and 90's?

You might give a look at some of the Fed's SSBF studies... in particular, 1987, 1993, and 1998.

FRB: SSBF INDEX

Also, this paper by Rebel Cole might put you onto something useful. Download the PDF version of the paper at What do we know about the capital structure of privately held firms? Evidence from the Surveys of Small Business Finance - Munich RePEc Personal Archive

Best of luck with the research!