Keyboard backlight switches off when daylight is above a certain level. This daylight is measured by the webcam. Is there a chance that, when you make your tests, some keyboard backlight hit the webcam and make the motherboard think the ambiant light is enough? Can you try covering the webcam with black tape and test again?
The PSU provides a permanent +5 VDC on the side connector. This same connector has an input, used to tell the PSU to provide +12 VDC on the 2 big metallic legs soldered on the motherboard. To make basic tests on the PSU you can: - remove it from the console - plug it in the AC with the power cord (from this point, manipulate the PSU only by touching plastic parts!) - connect a multimeter on the side connector and check that you get +5VDC on some pins (can't remember which ones, just test) - verify that you have 0 Volt on the 2 holes where the big metallic legs are supposed to be plugged in - use a wire to shortcut the first and the last pins of the PSU side connector, this should tell the PSU to provide +12VDC - check with the multimeter that you get those +12VDC on the 2 holes If yes, your PSU seems to be working. If +5VDC and/or +12VDC is missing, the PSU is the culprit. You can find tutorials on the net, just search "PS4 ADP-240 PSU Test" for instance.
If you teared down then reassembled with caution (I mean without applying force), you problably forgot something, or done something wrong, most likely with the PSU (power supply). If you have no beep at all, the +5V is missing. It is provided by the small 4 or 5 wire cable between the motherboard and the PSU. Check and report :-)
Sorry to tell that I don't think there's an easy/cheap solution. Facts are facts and you need to go from there. There's a heavy piece of metal that is driving the heat from the processor/graphic chips to the fan. It is strongly pressed to the chips to ease thermal transfer. When the console fell down, and from what you described, there's a good chance that this heavy heatsink damaged the chips and/or their solder joins, or even the motherboard. IMHO, the only secure solution is to have it looked at by a repair shop.
It all depends on the reference written on your optical drive daughterboard. Your drive can be a BDP-010, BDP-015, BDP-020, or BDP-025. Sometimes you need to remove the metallic cover to see the reference. Choose the replacement drive according to this reference and use your daughter board with it. However, BDP-020 and BDP-025 are cross-compatible (you can use a BDP-020 daughterboard in a new BDP-025 drive, or you can use a BDP-025 daughterboard in a BDP-020 drive).
These laser lens work at micrometer level, I doubt there is any way to fix them. A good option is to replace the whole optical block (the two lenses, rail, motor, ...). It's not very difficult if you are a cautious person, you will find a great tutorial here: PlayStation 3 Super Slim Laser Lens Replacement
BluRay drive is connected to the motherboard with 2 cables, a fex cable and a 4 or 5 wire cable. The 4/5 wire is providing power to the drive. Usually, with only the 4/5 wire cable connected, the drive should be able to accept a disk. Visually check this cable for any damage (wire cut, pin getting out of the connector, ...) Also check the connector solders on the motherboard if you feel you pulled too hard on it. Another possible culprit is the narrow flex cable connecting the 2 boards of the drive. This is responsible of giving power to the eject motor and sending gears positions to the main board. Testing the continuity from connector to connector (while the tiny flex cable is still in place) with a Ohm-meter would be a good option. If everything is fine, verify that the big flex cable, that links the drive to the motherboard, still has its 2 lock bolts on each side (4 total). If the locks are damaged, that means you didn't press the metallic tab on the connector before pulling the flex. A flex...