I would look right behind the seals to see if there are any cracks or at least evidence of the hoses being dry. There might not be any leaks per se, but the system is pressurized so any air at all in the system would cause temperature anomalies and cooling issues.
With any liquid cooling system, improper storage leads to problems just due to the nature of the liquid used to cool the system. Coolant in general is corrosive so it sitting in one spot or area in the system and not being circulated can cause issues.
I just think that it was stored improperly to the point where coolant stayed in the pump and what might be causing the pump to not pump it fully or in the off chance that the coolant has clogged part of the pump. After all, if the pump just wasn't working then the temps for CPU A would be crazy and that CPU would most likely be dead soon.
Yes there are but they are not cheap. If you do decide that replacing the LCS is the way to go, then I would forego using the coolant normally used and instead use mineral oil. It's not corrosive, not conductive, and can handle high temperatures.