In a friends truck we installed a modded xbox with Dolby Digital, 2 12"s, 3 screens . . . blah blah blah
When you installed the amps you should have had a power distribution block to get the power from the battery. The main power off the battery should have a fuse withing 18 inches of the battery and then go into the power distribution block where it is fused again and then splits off into various power cables . . . amp #1, amp #2, screen, screen, screen, whatever other stuff you got hooked up.
You should also have a Ground Distribution Block that all your amps and XBOX connect to. This distribution block is then grounded with a 2-4 Guage wire (depending on how much power you're using) to your car chassis in a spot that has been sanded down to expose the real metal. That will serve as your primary ground and prevent any ground loops and reduce road noise in the speakers (hopefully).
Also depending on how much cash you can get you can upgrade your electrical system. The guy we did the install for said money wasn't a problem so we went ahead and upgraded his trucks alternator. Thats kind of uncalled for but definately invest in an Optima yellow top battery, upgrade the wiring from the battery to your alternator (if you're using enough power to need a deep cycle battery it's gonna need to be charged more efficiently) and use some sort of daisy chain method to improve grounding from the car battery (this will also improve starts, shifting on an Auto transmission and make your headlights a lil brighter

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We also used a similar Pure Sine Wave inverter and we never experienced the problems they discussed in the other post. Definately check out the post Mr. Ed gave a link too.