One assumes the radio came with a copy of the owner's manual. If it didn't, you can download a good electronic copy of it from here: http://www.kenwoodusa.com/UserFiles/...als/TS-140.pdf
(I know it says TS
-140, but the TS
-680 is the same radio as the TS
-140 except with the 6 meter band added. The same manual describes both rigs.)
From what I can tell, the connector to use for the computer interface cable is ACC1. The 12-pin ACC2 connector is for hooking up a TNC for digital data operation (packet radio), and ACC3 is used for connecting to the optional AT-250 external automatic antenna tuner. The REMOTE jack provides some remote control functions (external ALC input, control relay, extra PTT input, etc...).
Looking at the rear panel of the radio, ACC1 should be on the right side, immediately under the ACC2 jack. HOWEVER, it looks like ACC1 isn't actually present _unless_ you have the optional IF-10C interface unit installed, like I mentioned previously. (See page 39 in the manual, where it lists the available accessories.)
If the IF-10C isn't installed, the hole where the ACC1 jack should be will be covered over (though the ACC1 label will still be there). You said there are three round DIN connectors on the back of your radio. With the IF-10C installed, there should be four. Since you only saw three, this likely means the your radio doesn't have the IF-10C unit.
That being the case, I think your only option is to buy the replacement interface board from Piexx that I mentioned before: TS140 Serial Interface Board - $89.00 : Piexx Company, Computers & Electronics
It may be a little more money than you expected to spend, but it's less hassle than trying to find an original Kenwood IF-10C on the used market. The good news though is that board gives you the interface and RS-232 connection all in one (you won't need another special cable). There's some pictures and installation instructions here: http://www.piexx.com/if10c/if10ci.html