If you have 1st and 2nd gears then I would think that the pump and converter are good. When I bought my 300D, it wouldn't change out of 1st, and the governor gear was broken.
Does park and reverse work? When it won't go past 2nd, does it just not change at all, or does it go into neutral? If it won't even try to shift, but stays in 2nd then there is a problem with the governor or the valve body. Both can be serviced with the trans in the car. If it goes into neutral instead of 3rd then it could be a clutch problem or valve body problem. The first test I would do is disconnect the kick down sol AT the transmission, remove any vacuum lines from the transmission and disconnect the bowden cable going down to the transmission. Check the cable and make sure it pulls out a couple inches and returns on its own. With the 3 things disconnected, it should still shift, early and hard through all gears.

Paul

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84 500 SEL (307,xxx miles)