Hi there! This thread has indeed became a valuable tool for us poor old romantics trying to keep their Sony DATs up and running.
Personally, I've been fortunate enough to obtain quite a few pro DAT machines, as they are practically given away by larger broadcasting companies. So I have a nice Sony PCM-7040, Fostex D-25, a bunch of Panasonics and so on. But what brought me here were two Sony PCM-2700s that were not working after sitting a while in the storage.
The Sony PCM-2700 is supposedly a pro version of DTC-77ES. It's an ugly, heavy thing with copper-plated chassis and two transformers. When I tested mine, the other one loaded the cassette but the playback was mainly digital distortion - you could tell what was playing, but that's it. The other one needed a new belt for loading mechanism to even suck the cassette in. After that, it sounded the same as the other one.
I did clean the heads, but it didn't help. So I started looking for hints, and came across this thread. Now, the mechanism in 2700 isn't exactly like the one presented by SaSi, but it has many similar parts. The discussion pointed out that Sony tape guides tend to need service. And indeed: the little thingies that are supposed to wrap the tape around the drum didn't quite finish their travel. To be exact, the left one was left a few mm behind the stopper. I pulled it gently during playback (with a cotton swab), and hey presto: distortion-free music!
Now, this thread taught me also that Sony lubricants are less than eternal. So I removed the mechanism as well as the PCB covering the bottom of it and cleaned the path of the loading arms with alcohol. Then I sparingly added new lubricant with a q-tip (high quality synthetic vaseline). I also took the rubber belt operating the loading arms and treated it with rubber rejuvenation stuff, and cleaned & lubricated most of the gears. After reassembly, I inserted a blank cassette and did some 20 load-eject cycles to break the mechanism in.
After loading an actual cassette, I noticed that the mechanical resistance of the tape had some effect on the loading arm travel. However, the repair proved successful, and my Sony now happily plays whatever I throw at it. In more severe cases, I suppose more dismantling and perhaps a new belt are necessary, but this did the trick this time. Hope this might be of help for someone with similar problem.
Take care, and keep vintage equipment going!