A B757's total air temperature (TAT) probe lost power after takeoff causing the loss of VNAV; LNAV; the autopilot; auto-throttles and other equipment; so the aircraft returned to the departure airport.

Narrative

My First Officer and I took off without any problems until 1;600 FT AGL and climb power with VNAV were selected. At that time we lost the TAT (total air temperature). The effect was also losing the lateral command bars; the LNAV; the VNAV; and all power setting indicators and limit markings. We also lost the auto-throttles and the departure depiction on the HSI. We continued the departure and climbed to 16;000 FT where we leveled off to determine what systems we had lost. We did the QRH procedure and determined that with icing on the entire East Coast of the US (which the QRH procedure restricted us from entering) and the fact that we had only the basic autopilot; altitude and heading; the appropriate action would be to return to the departure airport rather than proceed across the Atlantic Ocean. We briefed and got vectors to the ILS where we made a manually flown uneventful overweight landing and taxi to parking. We were told after inspection by the on duty Mechanic that the TAT probe had lost power and that had caused the other failures. The Mechanic replaced the probe the next day and we flew the aircraft uneventfully to our planned destination. I would suggest tracking the failure rate and time of these heated probes and replacement after a normal use time might have avoided our return to field.