The 1st attempt, I used the phpMyAdmin wizard. The 2nd time, I created it manually via the cPanel's mySQLdatabses tool (which by the way I've used probably at least 50+ times over the past 10 years, so I'm very familiar with it).
I always default to 'localhost', but when that didn't work, I tried the IP address the 3rd time. That didn't work, either.
I'm pretty sure I got the database name, user name and user password correct as it's the same ones I'm using for the live site under a different domain name. But I think after 3 tries with this version, and 3 tries with the previous version, and getting the same result... the problem lies within the install process itself. If I didn't have the credentials right, the install process should just fail with an error message, not just spin endlessly. That's always been how other installs I've done worked.
Either way... I can't keep burning the candle on this one.
BUt thanks for the quick responses!