Looking for Special Purpose IC

This is part of a motor control for an oil vent damper made by Field Controls.
I'm trying to identify the part labeled U1, and a source, if possible.

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The unusual layout of the part number threw me off. So any idea what the EZ numbers are? Usually the date code was the 4 digit number and the alph a numeric was the part number, but you're indicating this is reverse on SMD parts.

Every LM2904 sohc I have found has a clear labeling that makes sense. The IC in question does not.

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I'd be willing to bet on an LM2904, too, as it's cheap, runs on a single supply, and has the advantage of including ground in its common mode input range. The LS84 is a dual jfet made by Linear Systems, and it doesn't even come in the same package as the part in question. It's also not made by ST, and the part (U1) is definitely from ST.
 
Why do I think the IC is bad? Because it experienced a power surge and stopped working immediately afterwards. Semiconductors are sensitive to power surges. The rest of the unit is a Hayden timer motor and three micro switches driven by a cam on the motor shaft which tells the device the damper position and if the oil burner is calling for heat. Those components are fine.
 
Regulation might be via a simple buck circuit using an integrated controller. look for a bridge (or 4 discrete diodes), a 200V filter cap, and some sort of SMPS chip and inductor. If there is no MOV on the board, I would tack one on after the input fuse, as that would help filter out all manner of nastiness. If the buck regulator went south, it would likely take out all susceptible downstream semiconductors.
 
This is what the board looks like. I have two of these units that failed. This one failed one day when one of the micro switches got stuck. It made a loud pop when it failed. That was the sound of traces being blown off the board. The second one failed quietly, no visible damage. Just won't operate.

I have repaired the blown traces, but the unit continuously spins the motor instead of turning 90° and stopping.

This PCB is only about an inch and a quarter wide. It's too small for my eyesight to really see. The 120VAC comes in on the black and white wires. Orange goes to burner and yellow is the sense wire to the aquastat. Tracing this out to a schematic on paper is going to be tough, as I can barely see stuff this tiny. From what I can tell, there are some resistors a couple of diodes (D2?) and a transistor and 8 pin IC of some sort. Only one filter cap. Seems really minimalist. No surge protection whatsoever!

The cheapskates won't even tell me what the part numbers are!

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Do you have space to build a new one with better parts?
Or can you source an equivalent unit from a different supplier?

This one is, well, like @wrenchone says, not well made, only he uses a different term...

You need to do some work on this, work out the circuit, then check the parts, and replacing old SMD parts is a chore.

Best, quick, and easy fix is a heater / cooler dual temperature controller (common in plastic extrusion), with outputs for the heater / cooler, take them through SSR or contactor, and set the temperatures.
Use a thermo-couple or similar to sense the area temperature
About $100 here, you can find out what it will cost you in your area.
Be sure to add surge protection at the input and output sides..