If you managed to press the lightening cable form a iPhone 5(s) or 6 into the camera's mini USB connector, you must have broken the connector. I wonder if a repair is worth paying for, because the D60 is not that expensive second hand and a repair could cost over 200 dollar.
If you pressed the plug into the connector, some plastic parts must have come out, making it possible the metal contacts created a shortage. (Your battery will be empty by now) I can't advice you to do what to do, but I can describe what I would try if I had the same problem. First I would remove the battery, because some USB contacts could be connected to the battery. Don't make a shortage while the battery is still in.
Under a loupe with a bright light, I would try to pull out the plastic from the connector. Then check if and where a shortage is. I would try to undo the shortage and isolate the pins. Only then I would try to switch on the camera again, knowing I never could use the USB port again. If the camera would again switch on, I would again switch it off and remove the battery. Then taking care I would isolate all contacts forever, perhaps with some 2 component glue. Carfull not to connect points again. For transferring pictures I should use an external memory card reader and keeping the USB port closed forever.
It is a pity I don't have the D60 manual,because in the D50 the side where the USB connector is, is easy to remove, so you could even remove the connector from the camera, or disconnect it from the circuit board.
Everything hypothetical and don't blame me, if your camera never will work again.
I checked on iFixit, but they did not started a repair guide yet.
Nikon D60 Repair