How do I recover custom Content Types from SQL backup?

I find myself in quite a mess. Reminder to all....Take regular backups!

My problem:
I had to nuke my entire installation of Drupal, all modules, files, and the database. Basically start from scratch. Now I'm trying to get my site back to the state before the damage. But I have lost the content types I had created, permissions, users etc. When I go into Drupal its like a basic site.

What I had available.
A SQL Export of my database. A backup of my default/modules and themes directories.

What I did so far:
Reinstall Drupal from scratch. A brand new installation. Recreated a MYsql database. Note it has different user name (SQL) than the original database.
I configured the site with my modules and themes that I had saved. Logo setting etc.
Imported the data from my backup into the new database using Phpmyadmin Import.
rebuilt permissions

What I don't see:
The content types I had created do not exist. But I do see in the database the various field and node content names of my created types. I don't see the extra users. The database has 5 users defined to Drupal, but Users page only list one.

PROBLEM:Can I recover my Content Types?
I thought the database would allow Drupal to see and recreate my old Content types and fields. None are shown by Drupal. Can my content type and custom fields be recovered? Is this some kind of user (SQL) permission problem.

Help appreciated.

Perhaps I just have to enter the content types and fields from scratch? Hope not.

Thanks.