In my family room I have a series of 3 outlets that run along the wall. The 1st outlet has a timer connected to a table lamp. The second outlet has 4 strings of XMAS lights connected to it. The 3rd outlet has our television, DVD player, and satellite receiver connected to it. In the evening everything was turned on and operating. About 3 hours into the evening, everything went off that was plugged into the 2nd and 3rd outlets. No circuit breaker tripped. Thgis morning I turned the dial on the lamp timer and everything came on.

Is there some way to "increase" the power to the 2 outlets at the end of this run? Should I run a new circuit to handle the A/V equipment? Is that something I can do myself or do I need to call a pro?

Very common problem.

Check the connections on all the receptacles on this circuit, especially the one where the lamp is plugged in. You will likely find the wires just stuck in the quick-wire holes in the back. These connections routinely fail or give intermittent connections. By touching the lamp timer you are moving the device slightly. I bet if you wiggle the receptacle you can simulate the problem.

You should either move all the connections to the screw terminals on the sides of the receptacles, or replace them all using the screws, which is what I would recommend.