Funkpoliece is correct about the GFCI. If nothing is going to ground, nothing trips. From the look of your picture, it looks like the secondary side of the ballast, since that's where you connect the capacitor.
While I don't want anyone to burn their house down, in a way you can consider this something of a blessing. You now have a reason to replace those coil and core ballasts with electronic ballasts.
You ballast box will weigh a lot less, it will produce a lot less heat, and the savings on electricity will pay for the new ballasts in two to three years.
So get yourself a couple of new electronic ballasts, rewire the box, and enjoy your lighing upgrade, and lower electric bill.