This is pretty old technology and I have not personally encountered it. However, looking at the manual for the Link 1000 you should be able to see what is happening by means of the digital display, which can read current in/out of the battery, voltage, AmpHours consumed and time to run. Pressing the SEL button cycles between the 4 parameters to be displayed.
This will give you an idea of what is happening during various phases such as: Charging from the shore power: Charging from running the engine: Using the batteries to power stuff when moored.
If you can gather some data from that, ie current, voltage and Ah consumed along with a description of the circumstances, and preferably some photos showing it, then we will be in a better position to help, because at the moment your main complaint seems to be that the battery status lights are not reflecting the battery state of charge. It does sound as though the battery charging via shore power and alternator is working, and getting only a few days of power when moored is reasonable. So it could be something like a wire come off the Link 1000 shunt so the panel is not detecting current flowing. Anyway, more data about how the whole system is behaving is needed please.
Edited to add: I don't know how the system decides which coloured lights to illuminate on the battery status lights, but another possible explanation is that they are based on the expected State of Charge as measured by the amount of electricty taken out of the batteries vs their original capacity. If the capacity of the batteries has fallen significantly below the new value - as happens with all lead acid batteries fairly quickly, especially if the are over-discharged - then it could be that the Link "thinks" the batteries are still at quite a high state of charge when in fact they are nearly flat, due to lost capacity with age.
How old are the batteries and were there any events just prior to this problem eg excessive discharge or leaving the batteries fairly flat for a long period?
Anyway, a review of the current and voltage parameters during charging and discharging should give us more of a clue