Beginner PCB Repair - Voltage Regulator Issue
My best guess is that you have the new regulator installed backwards.  Easiest way to check is to grab the data sheet for both devices and compare pin-outs.  Conversely, grab the datasheet for just the to-220 device and make sure that the output pin goes to the line that you identified earlier as being the 5V rail.

Couple of things to consider.

1) there is a strong possibility that you have damaged or destroyed whatever is downstream of that regulator.  Most 5V-only devices can tolerate somewhere between 5.75 to 6.5 Volts applied to them before becoming damaged.

2) Check the data sheets for both regulators to ensure that you have the minimum output capacitance on the output pin.  The LM2931 is unstable with an output capacitor that is too small.  I don't recall if the minimum capacitor value is the same for the large vs small package devices.