Let me try. I will address the IC first as it is a very simple system. I will post a follow up on the more complicated possibilities with RCIC later.
The IC basically is a sytem to take reactor steam and condense it in a heat exchanger then route the condensate back to the vessel, removing heat in the process. The system runs on natural circulation. The steam rises to the condenser and is condensed. The condensate is cooler than the water being heated in the vessel so it flows back into the vessel. That is the theory. In operation all that is necessary is to open valves to allow the condensate to flow back into the vessel. The standpipe of condensate is kept filled by steam which is continuously available to the condenser. The condenser is basically a water tank that boils off and is vented to atmosphere. To keep it running all that is needed is to continue to add water to the tank. Since the tank is vented this can be done by a portable pump or fire truck.
Failure modes are azlso relatively straight forward. If the valve can't be opened the system won't work. At unit 1 the system was started, but apparently was stopped over concern about exceeding a design limit on cooldown rate. Later they tried to restart the IC, but it is not clear whether it worked. Power to the valve may have failed. The valve itself may have failed or the high temperatures in containment could have caused boiling in the condensate standpipe. This would have broken the driving force for natural circulation. Other possibilities are that the tank was damaged and leaked or boiled dry removing the coolant from the heat exchanger.
I have looked at the data dump from TEPCO from the first hour after the erathquake. It is clear that the IC was initiated and stopped after about 15 minutes. Following the tsunami there was no active instrumentation readings released so it is not clear what prevented reinitiation. The concern about cooldown rate was probably a mistake since the vessel was probably already on the way to core damage due to the extended SBO. I do think the mode of failure will be easy to identify when conditions permit examining the piping and valves.
Hope this helps. I will try to post on RCIC later tonight.