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GMUX firmware mod can still do brightness adjustment with either PCH microvia jumper (software and keyboard control, soldering is risky to perform), raw keyboard signal (no software control, some jumpers required) or custom driver (software and keyboard control, no soldering required), depending...
Why would you randomly reflow large BGAs for no reason? Good way to make sure to kill the board…
LVDS line issue, often caused by GMUX. Can also be a broken trace elsewhere or a bad LCD connector.
M1 needs to be working anyway since it contains encryption keys. You can still try to replace U8100, if you're very lucky M1 may be fine.
But first you can try to remove L8100/L8101/L8102 one by one to try to isolate the phases if there is only one shorted.
I think all the G84-603-A2 should have the good underfill yes (the white one).
Chip shouldn't get discolored too much when soldering. If it is, it indeed may have gotten overheated.
As 2informaticos said, profile will vary between rework stations but also between boards, so you have to calibrate...
Also be sure you got a good chip. Must have white underfill (not dark) and datecode > 0830 at least, model number G84-603-A2. Preferably "128-bit" memory bus, "64-bit" should still work if it's a good chip but it'll be limited to 128MB VRAM (it's probably a remarked G84-53-A2). Most chips on the...