I doubt if there is a significant current drain with everything turned off. So sorry you blew your Fluke's 10 amp range; easy to do. The thing is, to measure current it must flow through the meter so you must open the circuit (unhook a wire) and insert the meter in the circuit.
As a rough check for lost current, charge the battery well, wait overnight and see what voltage it has. 12.6 is fully charged, 12.0 is half charged. If it's only down a tenth or two don't worry about it now.
The jumper cables from battery to starter suggestion is really good; there undoubtedly is corrosion in the cable end connections. I bet you end up buying new cables.
Can you figure out if the engine is seized? Like pushing or pulling it in gear? My dads old tractor wouldn't start after sitting for several years, was seized. I put a quarter cup of light oil in each cylinder through the spark plug holes, left it for two weeks and it turned over. Unfortunately I tried too long and burned out the starting motor. (My dad was over 90 and could no longer crank it. When I was 18 I could turn that crank a quarter turn while he could do half a dozen. Old age can feel like hell.)
Consider the condition of the old fuel. Best to get as much as you can out of the lines and tank before attempting to start. I have no idea how to dispose of it - ask at your recycle center. I hope it is old enough to allow a siphon hose into the tank and has the fuel pump outside the tank. Carburator? Injectors? Fuel pump? Filter? Worth getting professional advice or help before attempting to start it again!
