Then sounds like most likely the ICM. If your new one doesn't come with heatsink compound, AutoZone stocks some:

https://www.autozone.com/miscellaneo...1-ea/19189_0_0

After removing the old ICM inside the dizzy, scrape/wipe off any residue of old compound (if there isn't any, that may explain why it failed), apply a thin, even layer across the base of the new ICM, install it, then wipe off any compound that squeezed out of the edge. Don't just use dielectric grease, as that isn't doped with thermally-conductive particles like proper heatsink compound is.