How do I change the color black

Question

I will preface this by saying I am new to Photoshop.
The Problem? I have a family logo on a solid black background.  This is not a photograph.  I want to change the solid black background to a custom green color.  This sounds simple enough, but I cannot get Photoshop to change the black to green for me.  Here is what i have tried so far.
1.  My file is a 16-bit RGB TIF file.  I have saved the file as a RAW file and a PSD file and neither of these work.  So I assume the problem is not the TIF format.
2.  I have tried this.
     Image -> Adjustments -> change color.
     I can use the eyedropper to select the black (in the background) and the preview shows the black selected.
     However, when I move the HUE slider below, the color stays black.  It does not change color.
     If I type in the Hue Saturation and Lightness numbers for my color, the background will change, but it changes to gray, not my color.
3.  I have tried this
    I set my background to the color I want.  (A custom color I created, of R:34  G: 139  B:34)
    I click on  BrushTool  -> Color Replacement Tool
    Settings on the horizontal tool bar are
        Mode: color    Sampling: Once     Limits: Contiguous    Tolerance: 5%
    I then click on the black background, but it stays black.  It does not change to the color I specified.
    (I have also tried Discontiguous, different modes, different sampling, etc. Nothing works).
    I will note that if I set my background to blue (R:0  G:0  B:255), then the Color Replacement Tool works.
    It will change the black background to the basic blue color.
    It just will not work for the custom green color that I created.
    It also will not work for most of the other default colors in PHotoshop.
This is probably trivial for some of you, but I have spent a couple hours listening to tutorials on youtube and trying various things, and I am stuck.  Would appreciate your wisdom.

Answer 1

I would like to thank everyone for their kind suggestiosn and insights.  I will try your suggestions as learning exercises, since I am still very wet behind the ears on all this stuff and the more I can learn and know, the better. 
Good news is that I was able to get my background to change from black to the green color that I wanted.  I utilized a two-step process that dawned on me after I responded to Curt Y's first post.  Realizing that I was able to change the black background to a blue on an earlier try (though it would not respond to my attempts to turn in to the green I wanted), I thought it might work to change the color twice - first to a color it would accept, and then from that color to the green i wanted. This process worked.  I probably would not have thought of this without the comment from Curt Y, who got me thinking outside my box. 
Thanks again ... and I will try your suggestions because they will teach me new things and some of them are likely simpler than what I did.