The ballast feeds the coil not the electronic box.
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The ballast will get hot but should never get "red hot"
I suspect a bad coil or a shorted wire between the ballast and the coil positive.
Disconnect the positive coil wire from the coil. Put some tape on it so it can not short to anything.
Remove the same wire from the ballast and check with a multimeter to see if there is a short to ground on the ballast end of the wire.
If it shows OL (or whatever your meter shows when measuring resistance and the leads are not touching anything) than the wire is ok
Next would be to reattach the wire to the ballast and turn the key to run.
If the ballast gets hot than there is something behind the ballast making contact with it to the body.
