For one thing, you need to reimport the game model so that it has its original UVs. When you use the Unwrap operator, it replaces the UVs of all the faces that you've selected with low-distortion, unique UVs. This is probably not what you want to do if you're just modding the texture.
Once you've got the model reimported into Blender, the next step is to make sure that you're using Blender Render. In the top bar of the program there's a dropdown that might say "Blender Render", "Cycles Render", or "Blender Game Engine." If it's not on Blender Render, click on it and change it to Blender Render.
You'll need to set the viewmode of your 3d viewport to Textured. This can be done with the hotkey Alt+Z by default, or there's a dropdown menu with all the view modes in the bottom bar.
The next step after all of this is done is to split the 3d View so that you have a 3d View and a UV/Image Editor. Open up the texture in the UV/Image Editor and enter Edit Mode in the 3d View. Select all of the faces on the model with the A key, then if the UV/Image Editor switched to a blank image go back to the UV/Image Editor and switch back to the texture you wanted. This sets the active texture for all of the polygons on your mesh to be the one you wanted to edit. Now you can exit Edit Mode. You may want to open the N Panel in the 3d View, go down to the Shading section, and set shading to Multitexture and turn Shadeless on. If you decide that you want some lighting on the model so it's easier to see the shapes, I recommend using a Hemi lamp as that will show you the models shape while lighting it entirely.
You can change the UV/Image Editor from View mode to Paint mode in the bottom bar and use the T panel to pick colors. This way you can paint on the image in Blender. If you decide that you need to go back to Photoshop to do your painting, you can easily preview what it's going to look like on the model by saving the PSD, loading it into Blender, setting it as the active texture, and resaving the PSD from Photoshop whenever you need to view the changes, going back to Blender and using the hotkey Alt+R to reload.