It took me a while to figure this one out.

I migrated from my old hosting site to ICDSoft. On ICDSoft, I created a MySQL user with a similar type of password (all numeric) to what I had used in another non-Drupal project.

It seems that setting my MySQL password to a numeric only password caused Drupal to fail the log in. Setting it to alpha-numeric fixed it.

If running mysql, the error generated is:

Access denied for user 'henry'@'localhost' (using password: YES)

Worse, though, when running mysqli (which is what I was running), you get no error message from MySQL.