ok, i'll start with the neumonic, bad boys ravish our young girls but violet gives willingly.
there is a racially insensitive one i grew up using.
black brown red orange yellow green blue violet grey white
BBROYGBVGW = 0123456789
black =0, brown=1, red=2. 0range=3, yellow=4, green=5, blue=6, violet=7, grey=8, white=9
the first 2 numbers give you the first 2 digits of the resistor value and the 3rd band is the power of 10 multiplied times the first 2. make sense?
so BlueRedBrown=621 or 62x10^1=620, OrangeBlackBrown=30x10^1=300R or 300 ohm.
that's all it is.
the 620R resistor is not part of the input power resistor. it helps the voltage regulator drop the voltage to the 12V rail by diverting some current through the resistor instead of the voltage regulator.
does the gray one have anything printed on it? that is the input power resistor, there should be more than one to absorb the heat of the power dissipated. you could replace it with 220 ohm 2W resistor and likely be safe at 30V. assuming 65mA as the controller current, then the 220R resistor has .065x220=14.3V drop so the regulator will see 15.6V, at 300R that is only 10.5V which will still run, but not very much voltage for the circuits that need 12V out of the regulator, which would only be about 10V then. but if the controller current is only about 55mA then that is more like 30V-(.055x300)=13.5V input to the regulator which is ok. just barely ok.
that's all there is to electronics. it really is pretty easy to read them once you start practicing.
these are 10% resistors.