okay, so you seem hung up on the kickstart. so, let's eliminate that.
see the yellow circle? that's the kickstart pinion, remove it.
if the lever is flopping around, the return spring is likely detached. don't worry about it, just yank off the kick lever. everything is contained by the plate on the inside of the trans cover.
ET's are notoriously difficult to kickstart anyway and people usually just wind up cracking the trans cover. so just leave all that mess be.
anyway, see the pink circle? that's the crank nut. it's 18mm, get a socket on there and see if you can turn the motor over. make sure that the starter bendix isn't jammed up in the ring gear teeth of the 1/2 pulley.
if the motor turns over, then snap all that back together and pull the starter and test that. check the starter relay for corrosion and clean as necessary. because it sat, and it's from the Bay Area the inner contacts might be corroded, so sometimes a replacement is a cheap bet.
on the battery. new does not mean good. have it load tested. it can have the volts but not the amps to crank it over.