Number one thing to check is the TV bushing. It's the bushing up near the throttle body where the cable that goes down to the transmission attaches. That cable tells the transmission how far down the accelerator pedal is pushed, and so it varies the line pressure. The problem is that those bushings are made of plastic, and after many years of heat and vibration they tend to go to pieces. When that happens, the cable falls off and the transmission defaults to the lowest line pressure setting, and your transmission burns up REAL fast.
Here's an article that talks about how to diagnose the problem and how to fix it:
Lincolns OnLine | Tech Tips and Articles
Oh, and if you've already caught this seller in some lies....I'd be VERY wary of buying it. I'd be very tempted to steer clear altogether.
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1989 Ford Crown Victoria Police Interceptor
2bbl Carbureted 351W V8, ported and polished E7TE heads, Edelbrock cam
AOD Transmission with B&M Shift Kit
3.55:1 Positraction Rear Axle
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Updated 1/27/07!