I have a Sony PCM 2700, Sony A8, Panasonic SV3800, and HHB PortaDat, and only the last one now seems reliably to play my old tapes, regardless of which machine they were recorded on. The rest mostly just spit out digital hash, giving the impression they are simply unable to read the tapes. My point being that you may find that a perfectly good DAT deck may not actually play your old tapes, due to perhaps some kind of tracking differences or whatever. I don't know whether there's a standard technique for fixing such problems?
[Edit - it occurs to me that a sensible buying technique would be to select one of your old tapes in typical condition, but one that's not too precious in case it gets graunched, and take that with you with a pair of headphones to anyone who offers a machine for sale, to test compatibility. If dealing with someone here, I guess you could send the tape and trust them to test it.]