Is the old 5V router power supply regulated? Is it a wall wart? How many milliamps does your project need? How many milliamps can your power supply give. How are you providing power to the fingerprint scanner and the servo?
Microcontroller, fingerprint scanner and servo all runs of the same power supply and peaks at around 125 milliamps.
I have no idea if the power supplies are regulated or not, are there any easy ways to check? The router supply can provide 2,5 amps and the phone charger 550 milliamps.
That circuit doesn't seem to have decoupling capacitors on it. Try putting 0.1 uF between VCC and Gnd (pins 7 and

and also AVCC and Gnd (pins 20 and 22). I'm guessing your router power supply is a bit noisy.
For the router supply this didn't work. It worked as it should up until the servo was in "door open position" and then the reset happend. However if I used the phone charger with the capacitor it worked as a charm, at least with initial testing.
Only difference between them is that the router one runs effectively at 5,17V and can provide 2,5 amps and the mobile charger runs at 4,95V and can provide 550 milliamps. So why would the phone charger work and not the router one?
Another weirdness is that when I checked the current drawn with my multimeter, using the router supply, everything worked as it should, only slower. Blink was slower and servo rotated slower than usual. Why is that?