Glad you've got it sorted.
A few often overlooked pointers here ..............
is on the right track here
A Battery always needs testing under load, and not with Multi-meters either ........... (Heavy Discharge or "Drop" Test).
If OP's Battery with it's 12.8 Volts had been Drop Tested it would have likely read 7 - 10 Volts Max ....................
On any Car with Electronics that is simply not enough .
On a more advanced Car like say a W220 S Class, W210 E Class etc, the Electronics will throw low Voltage Codes if the Battery drops much below 11.2 V and it will not even attempt to Crank !!
A V6 and any Post Facelift R170 will do the same.
On the "older skool" 4 Cylinder pre facelift R170 it still has more Electronics than most realise and will still need a good strong Battery ..............
Just because a Battery starts the car doesn't mean it is not at the end of it's useful life, R170 has Modules that will not be happy with low Voltage, the TCU is a common example of one to go into limp mode over a low Cranking Voltage
HTH, Cheers Dave