This would have been good to know right off the bat. An HEI would necessarily be wired completely different from a stock ignition.
If the stock wiring harness was still used, some things would be the same, but not all. Since this has a Centech harness in it, you might need to trace a few wires to make sure it's still valid.
At the starter relay, you will have a Violet (purple) wire on the S terminal. On the other small terminal (usually marked with an "I" for ignition) you "might" have a White wire. If you do, and that wire is connected in the harness, then all of the previous suggestions are still valid.
If not, you may have some digging to do.
Luckily, the way yours is acting is consistent with having the White wire connected to one of the Blue wires near the passenger side rear corner of the engine compartment. If the Blue wire then goes on to power the HEI distributor, then the other Blue wire from the harness (from the ignition switch) is not getting it's signal.
I'm pretty sure (but not 100%) the Centech fuse panel has a fuse for ignition duties. Better check all of the fuses while you're digging around just to make sure you're not simply fighting a blown fuse.
Of course, then it's the fun time finding out what blew it originally!
Oh, and last question for now... Is this a real HEI ignition with the big GM style cap and the coil integrated on top? Or is this an "HEI" (as in high-energy ignition) maybe from a Ford Duaraspark or other aftermarket style?
Thanks
Good luck.
Paul