I am looking at picking up a decent 1987 cabriolet with 90,000 miles that is being offered for sale at a low price ($1,000) because it won't run. The motor turns over and will run for a short time if starting aerosol is sprayed in the intake. Makes me believe it is a fuel starvation issue. What is the likely cause? I am hoping it is a simple problem like a bad relay. Any thoughts? I plan to go out there again this afternoon.

When you turn the key to on position listen for the fuel pump. If not, it's most likely the relay or pump itself.