Stickman, both O2 sensors run off a circuit that includes many others...there is a generic 'engine' fuse inside the drivers side door, but if its blown the engine will crank...but will not start, and you're water temp gauge will spike to max (a mechanism to point to the fuse being blown)...
Tweety is right about the heaters; they're internal. I'm seeing 'bank 1, sensor 2' for p0037 in various code databases, which would point to the 2nd o2 sensor according to most descriptions... the first o2 sensor uses an internal heater to speed up its own warm up, thereby getting more accurate readings faster than it would take for normal exhaust heat soak. The 2nd sensor uses a heat sensor to monitor catalyst performance.
The first sensor isn't part of the emissions system...its part of the engine control system, and when it goes, it will create noticeable driving problems. I'm assuming your second sensor is bad, and that your cat is fine...
