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I have the impression that the varnish has overheated on the trace connecting the SMOOTH chip to the 3R3 coil. Does this seem suspicious to you?
Overheated varnish looks different - it takes on a dark yellow or brown tint, depending on how hot it was. I can search my archive for photos of what this looks like if you're really interested, but what you see in the photo isn't evidence of overheating, but corrosion - moisture has gotten under the varnish. Scrape it off with something sharp and metallic, and the varnish will easily peel off, revealing oxidized copper underneath.
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What do you think of these results?
I think the board is completely destroyed, beyond repair. Why is that? The ROM chip should have 1.8 volts on one of its contacts. Why exactly that much? Because next to the ROM chip, there's another rectangular chip without pins, made by Samsung. This is DDR2 RAM. It also operates at 1.8 volts and must be powered; without working RAM, the microprocessor won't work. To reduce production costs, chips were selected that operate at a single voltage, which is standard practice for such boards.
One of the required voltages is missing. More precisely, there are no necessary voltages on the board at all, except for those coming from the power connector. The SMOOTH chip is responsible for all the voltages and all the hard drive components that need to be moved. That's why it's suspected of being faulty. It's possible that it's not the chip that's faulty, but rather a component nearby, but for further diagnosis, we need to measure what's feeding this chip.
This chip doesn't have any pins accessible for measurement. There are small yellow elements near the chip. On some of them, at one of the contact pins, there are 5 volts and 12 volts coming from the power connector. You can also take measurements at the yellow dots with drilled holes if you cannot find the voltage on the capacitors. Considering that there was a tiny voltage on the ROM chip, these voltages were likely coming into the chip.
And now the real problems begin.
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Is this difference normal or does it indicate a specific issue?
This is an internal measurement, so it's difficult to tell whether the diodes are intact or not, but common sense dictates that these diodes don't usually fail, and certainly not two at a time.
The real repair begins with a visual inspection. We've already seen the damage in a place where it shouldn't have been, so the procedure begins by checking all tantalum capacitors for short circuits and resistors for deviations from their nominal resistance.
Since, again, all these measurements are performed internally, some resistors will have unusual resistance values, just like capacitors, even though they shouldn't conduct current. The problem is compounded by the fact that an analog meter isn't very suitable for these measurements. Of course, you can diagnose a board with it, but you'll have to use the same measuring device to take measurements on a working board. I probably have a working board with similar components, but if I measure it with my digital multimeter, the readings will differ from the analog one because these devices supply different voltages for measurement, which will lead you down the wrong path.
In a real repair, the quick and correct step is to replace the SMOOTH chip with a working one, or install the suspected faulty chip on a working board. Further actions depend on the outcome - either the faulty chip was the problem, or the board itself. If the board is the problem, then all components and contacts are checked against the working one, and the discrepancy will sooner or later be found, and with it, the source of the problem.
What do we have in the end? We can't take measurements on the board because we don't have the right equipment, there's no donor board, and there's no way to quickly diagnose the board by replacing the suspected chip. I'm missing the point that this particular chip on this board is difficult to replace because it's soldered onto lead balls underneath.
As a last resort, it would be worth looking at the back of the board for damaged traces.
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data recovery will become extremely expensive, if it is possible at all
This was meant to be a learning project, not a case of data recovery or disk operation (yeah, ST3000DM001, the old legendary Grenadas that failed en masse due to low-quality manufacturing), and judging by the condition of the drive and the fact that the sticker where the screw of the magnetic head unit is hidden was torn off, the hard drive had already been taken from a trash heap.