After the program runs for like 10-20s,
Note: I had been running the Arduino with a 4.8v battery connected to a shield, so it wasn't going to the power pins directly, but into the positive and negative ends of a digital pin.
I connected the battery to the negative side, which would be the board's main ground, and the positive connected to the digital pin.
If you connect the positive side to a digital pin and the negative side to the ground, the board turns on. It has done this for 5 months for me.
I had worked with r/c equipment. The receivers used can be powered from any set of pins on them, and I figured this worked the same way, which it did. The biggest problem is that I don't know what the "L" light means. I already ordered another Arduino Mega (the newer one) because of time constraints. I can't spend more time on this one. I need to know what the light means, though, so I don't make the same mistake with the next board, though I won't be powering it the way I have been.