Will a new LCD 52 inch Sony TV plus a receiver and DVD player overload a 15 amp circuit?

Not likely. Add the (Watts) of each and divide by your mains voltage. That will give you amps. Mains in the US are 120V. 1200W = 10A, @ 120 V; 15A @120 V is 1800 W, so I seriously doubt it.

Take a look at the power requirements on the back of each device.

I just went to the SONY website and looked at a few 52" LCD TV's. The most power hungry device was 400 watts max load.

A Satellite Receiver from Sony was listed at 40 watts.

Unless your DVD player is incredibly power hungry, or there are other devices on that circuit, you should be OK.

A 15 amp circtuit is good for more than 1500 watts. (Think hairdryer or toaster).

You are using a surge suppressor on your system though, aren't you? I would also suggest looking at getting a UPS device that regulates the voltage (keeps it constant) to make your system even better.

Good Luck, Dan