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I had this same compression check problem years ago. The screw in compression gauge has a schrader valve that broke / wore out and would not hold the gauge pressure reading. On compression stroke the pressure would go up and then blead to "0". If you are cranking the engine using the key in the cab, the gauge will blead to 0 before you can look under the hood at the gauge. To test the gauge, watch gauge while cranking engine from under the hood.
Maybe your new battery is turning the engine over so fast it just sounds like an LSD flashback. If the cam is turning the valves are working too. The question posed earlier was never answered. Was this engine running before the battery swap? If so, given what we know, there would be no reason for the compression to go away. It would help to post a video of the cranking ceremony.
Sounds like the engine internals are turning. Have you removed all of the spark plugs as advised in an earlier reply? Crank engine from under the hood while holding your thumb over the spark plug hole and feel the compression in each cylinder. Evan as little as 15 - 20 lbs pressure should record on the compression gauge. Can you test compression gauge on lawn mower, chain saw or another vehicle to verify it is working correctly?
... If the cam is turning the valves are working too. ....
It is common for flathead valves to get stuck open after periods of inactivity. For at least one on each cylinder to stick at once, seems unlikely but looking thru the plug holes to see if they are moving would verify.
Thumb over the plug holes would be a quick check on compression.