Power Issues

I'm using a generic MEGA. My project runs fine off the USB port but when I use a 12v 2A wall wart, the MEGA turns on and off.

The project uses a RC servo, a 20x4 LCD, 3 LEDs, 2 RGB LEDs, an Adafruit MP3 board, 5 pushbutton switches, 2 50mA sensors.
I could try running some of the devices on a separate 5V power supply and not off the MEGA.

So far, I've tried using a different MEGA, using a different wall wart. Checked the wall warts under load to another 12V device and was getting 12.1V.

My thought was that the USB port is limited to about 500mA and the project should work fine with a wall wart.

I guess I could try a third MEGA and see if the problem is the same.

Just wondered if the experts here have an idea?

The project uses a RC servo,

That spells trouble due to the interference it kicks out.
Try some supply decoupling.

Thanks, Grumpy,
I'll give it a try.

Just an update.

I used a surplus power supply, that I'm guessing is from a computer. My project worked great; no power issues.
The power supply used is an Artesyn NFN40-760. I ran the RC servo and the common anode RGB LEDs off of the 5V output and ran the Arduino MEGA off the 12V output.

Next I was going to try a 12V choke on my 12V wall pack and see if that fixes my problem as well.