No Electrical Power. Zero.

I'd say it started out as a bad alternator and when you replaced the battery you created a new problem. Did you verify the battery has power?--I've bought new dead batteries, it happens. Most likely it's just not getting a good connection. Cables and terminals clean, in good condition, and tight? Turn something on and wiggle the cables/connections to see if you get any action. Any chance the battery was connected backwards, even briefly?