You need to go through your kit and trim back all those leads that are sticking out, then reflow your solder joints. More heat will be very helpful for all the joints in your amp other than the power switch and the LED connections.
There are many, many causes for the LEDs to not light up other than the LED itself, but if you endlessly resolder them you will melt them and they will need to be replaced. If that happens you will have high voltage on either terminal 1 or terminal 5, so for now leave those LEDs alone and focus on the rest of the kit.