Check PP3V3_S5 & PP3V3_S3. Put old U7201 back on. You were on the right course, but the problem was not U7201. PM_SLP_S4_L is missing because of a dead MCP79 and that is why PP5V_S3 is not turning on.
The signal from MCP79 going to Q7210 to keep the ENTRIP signal of U7201 low is not present. Remove Q7210 and see if PP5V_S3 shows up with old U7201.
Short on PP5V_S3 is always possible and something to check for, but I sincerely doubt this is the case.
Either way, this is old trash, I would junk it. If it is MCP79 you cannot find this anywhere new, just used, so you will have to do BGA rework and pray that the chip you get actually works. Further, this thing with a GPU is shittier than new machines with integrated graphics, and it is worth like $400 when it works. I would just toss it.
Also, double check if a short has appeared on PPBUS_G3H. 1.7v is the circuit going into a protect mode when there is a short on the bus, the charger will only output 1.7v instead of the standard 18.5v. My guess is in soldering the new U7201 that PPBUS_G3H got shorted to ground. There are two caps right next to each other for PPBUS_G3H & something else around U7201 that are really easy to short together. Clean the area of any flux residue and look at it under a microscope to see what happened.
Even though you completely failed to fix this, you are actually using your brain to obtain the knowledge and resources required to solve your problem. You are making progress instead of waddling helpless, I hope others follow your example!