If it's truly 0.8V, then that actually points away from the battery as Brian points out. A completely dead, worn out battery will read like 10.5V to 11.5V. Those are batteries that beyond discharged and probably goners. That is something of an odd value for another reason, that's close to a junction drop. Not sure what could be big enough to flat a battery and still measure 0.8V without burning up, so I suspect that measurement might have been an error if all your connections turn out to be solid.
Dielectric or terminal grease is the right stuff. You can smear regular grease all over the terminals after you've made the connections, that's a good idea to prevent corrosion. But only conductive grease should be between the terminal and connector.
If there was corrosion around the battery it's possible the ends of the battery cables are corroded and partially broken. If you can, measure the voltage at the terminal of the starter, it should be within single digit millivolts of the measurement at the battery. IOW, with a DMM you should see 12.30V at the battery and maybe 12.29V worst case at the starter.
It's also possible the battery itself is broken, the plates inside are bussed together to the external terminal. Optimas, especially their side terminals, suffer mechanical breaks that cause them to open. With the Optima its often because people wire their winch to them but internally they are not connected with substantially large enough strips of copper and they melt open, literally like a huge fuse. Anyway, maybe the terminal is making intermittent contact. Measure with a voltmeter and twist and shake and bump the battery to see if the voltage drops out.
"Why does the U.S. care which flag will be hoisted on a small piece of land thousands of miles away?" -- Ron Paul