Yeah, maybe the bleeder, maybe the cap. Can you see where the overflow is coming from? I'd start with a new cap and I'd take the 8 screws out and look at the bleeder valve top but I wouldn't replace it unless I saw something obvious. Also I'd fill the tank and bleed the system with the valve until the temp came up enough to run the fans. Then I'd close the bleeder and see what happens.
Do the radiators get hot? If not you'll need to fix that first, either air in the system, a bad water pump (the plastic impeller can break) or something else that is keeping the coolant from flowing. If the radiators get hot it probably something with the cap or valve. On my 2000 S (bought it in December) I replaced both the tank cap and the bleeder valve cap only to find my leak was actually coming from the o-rings under the bleeder valve housing, but mine wasn't leaking as much as yours so they might not be the same issue for you. Here are a couple of pictures of my bleeder valve and the o-rings in the event you find a need to go that far.
The bleeder valve cap after removing the 8 screws.
The bleeder valve housing under the cap. This piece lifts straight up but it's very tight and you'll need to wiggle it with some big pliers to get it loose. You can see my new pressure cap with the suffix "04" signifying the latest design revision.
Underneath are 2 o-rings. They are laying loose in the picture but in real life they fit over the respective openings. New ones fixed my leak.
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