The absolute first thing I always check, is the ground side of the battery where it is bolted to the chassis. If it's a bad connection, everything goes south and don't come back. I check it by removing and cleaning the connection. This connection often corrodes, and usually nothing looks wrong. You can use the multimeter to check it, disconnect battery, and check resistance between negative battery lead and the chassis anywhere. It should read nearly zero resistance. A bad alternator output, like one with a broken coil set wire, will work fine right after you charge the battery, and run the battery down till you charge it again. At least that's what mine did. It definitely needs traced with that multimeter. Either there's a short or an open resistance drawing current away. Sometimes checking for a short at the fuse box with the multimeter is quicker. Although things that run with the key off, like clocks and alarms, will give a false reading. You really need a schematic or wiring diagram to do this. Shorts are going to be found by unplugging stuff till the problem goes away. If it's as bad as you say, probably don't even need the multimeter to do that. The multimeter would only say you have a short, go find it. Sometimes popping fuses out will isolate which circuit is the problem. I found one like this at the fuse box. The main fuse holder was copper, and brown from age. It was hot, too much resistance. Cleaned it and was good to go. And oddly enough, the key switch itself is a notorious place for a short to occur. Usually discovered by jiggling the key and having things flicker or act up. And then there is the other stuff. The engine doesn't want to start, but how is everything else? Headlight work? Horn work? Horn weak when brake light is on? Headlights nearly go out when trying to start? (more than normal anyway). It might be possible to narrow it down to the ignition circuit connections and parts, if everything else acts ok.