Method #1:
1. Rigid Joint the cover into place as you had already done.
2. Take measurements X and Y measurements between some corner of the appropriate hinge's face and a nearby corner of the cover's face.
3. Undo/delete the Rigid Joint created in step #1.
4. Create a Rigid Joint between the corner of the hinge you measured from and the corner of the cover you measured to. The cover should move up to the hinge, but of course it will not be located properly over the box.
5. While the Joint dialog box is still open, enter the measured values into the appropriate Offset fields. This should get your cover located correctly centered on top of the box as desired.
Method 2: (This method assumes the sketch will move with the cover component when you delete the first Joint. I haven't tried it. It might not work as I'm imagining. I just brainstormed it up as something you could try.)
1. Rigid Joint the cover into place as you had already done.
2. Make sure the cover component is active.
3. Make a new Sketch on the hinge-side face of the cover.
4. Project into that Sketch the hinge's screw holes.
5. Finish the sketch.
6. Delete the Rigid Joint made in step #1.
7. Rigid Joint the cover to the hinge using the center point of a projected hole in that Sketch to the appropriate center point of a hinge hole.
(This method assumes the sketch will move with the cover component when you delete the first Joint. I haven't tried it. It might not work as I'm imagining. I just brainstormed it up as something you could try. If it doesn't work, you may instead have to make the sketch on the rear of the cover while it's in its original location, and manually place points in the appropriate positions with dimensions from a corner reflecting the appropriate place that will match up with the hinge holes.)
It's much better to export the file as an Archive *.f3d and attach that to the thread.