Is the grease that's used on the big computer just common dialectric grease or something else?

Mine's as clean as a whistle. always has been. I could understand somebody putting a light smear of something to keep torrential rain out, but it's not the norm.

There was never any grease put there from the factory. I have come across connectors like that where dielectric grease has been used but if the seal on the plug is working properly it should not be needed.
I would suggest removing all the grease and dry it out then put a new seal in place. Often the plugs don't get seated correctly and water gets in so the owner or the mechanic thinks the seal is not adequate and throws some dielectric grease in where correctly seating the plug would have done the job.

A similar grease called "DC-4" is used in the aviation industry.  It displaces water, and causes no harm.  I use it on battery terminals, to ward off corrosion.
Thank you!
John in Phoenix

I use this, it is a very good product for all electric connexions