You can look at the ignition switch and it's harness and I would also try to get a look at the back side of the fuse box in the dash to check for chaffed and shorting wires. But, you're probably going to want to pull the dash to really get a good look at all that wiring... unless you find something simple like an amplifier or other power wire poorly routed through the firewall - without a grommet for example.
I've seen several fuse boxes with shorting wires on the back side of it like this one....
If you're feeling brave, you can try it some more and see if you're getting 12v at the coil with the ignition switch in the 'ON' position. If not, then you have a starting point. But it's not going to fix itself and is going to need some repair whatever/wherever it is.
Does it smoke in the ON position or just when you tried to crank?
Anyhow DIY wiring mods from a previous owner that might be suspect?