Thanks for the suggestions all. I got it solved, but I'll detail how, to save other people time.
Okay. Zarcon, to clarify: when I attempt to create an album, it tells me "Album was successfully saved". Underneath that message is a box titled "My Albums", which is supposed to then show me that new album I had created. That box remains empty, without any albums listed in it. Until I create those albums, I can't seem to upload pictures. The album needs to be there first. Unless, of course, I'm adding profile photos, but that wasn't working either.
Sydeburnz: I disabled the promotional membership when I started configuration of Dolphin. I only have the Standard account, and the Non-Member accounts. The test account I created is a Standard account, and has all photo permissions turned on. add, approve, etc.
Houstonlively: Checked and autoapproval was turned on.
Now, as for what I found. I was trying to create an album called "Tattoos". I tried several times, and could not create it. After checking and rechecking my permissions, I tried one last time, just because I'm stubborn, and created an album called "Test".... Well, it worked. And I could even add photos to it.
Then I tried to add a Profile Photo. It disappeared into the mists, nowhere to be found. Well, I went back into My Albums, and found a little tab called Disapproved. The Tattoo album I'd tried to create, as well as the default User's photos album, were both in there. I went to the Photo Module in admin, and tried to Approve the photos, with no luck. The pictures still didn't show up.
So, as my test user, I went into the Disapproved Albums, and deleted those albums. I am now able to create a Tattoo Album, and a User's Photo's default album, and upload pictures to them without any trouble. As to what I did to cause this in the first place, I can't tell you.
Regards
Chris Robock
www.youmademeink.com