short-circuit
I was installing a RV roof vent fan and accidentally shorted it (connected it in reverse polarity).
The short seems pretty clean and I was able to manually confirmed that nothing else was broken by manually bridging the short with a piece of wire held in place.
I was wondering what the easiest way to fix this would be (I'm more of a software than an hardware guy)… I was thinking maybe I could just put a bead of solder where its broken?
So you have a bi-color LED for which both colors are known to work when connected to batteries. You've asked for a way to connect them to a motor such that the colors indicate the rotational direction.
What you haven't specified is how you are powering the motor (same two AA batteries?). You didn't specify how you are reversing the direction of the motor (is it a mechanical switch or transistors?). That's the purpose of a schematic: to illustrate how everything is connected.
You should definitely invest some time and effort into learning how to draw a schematic. It doesn't have to be fancy, and it doesn't even have to be drawn with software. You could draw on paper and take a picture. Its whole purpose is to communicate to other electronics engineers what you have in your circuit. Have you heard the phrase "A picture is worth a thousand words"? It's never been more true than in electronics as far as schematics are concerned.
So let's start with an LED. This is a light-emitting diode, so it uses the schematic symbol for diode plus two arrows to indicate light.
Your 2-color (bipolar) LED is two of these with either the anodes or cathodes tied together (this diagram is common anode):
I'll assume that your motor is designed for 3 volts. Even though you can light the LEDs with this voltage as well, you should use current limiting resistors to prevent the LEDs from burning out. Without knowing specifically what LEDs you are using, we will assume that each color \$V_f\$ of 2.2V, a common value for red/green bipolar LEDs. We will also assume that they have a standard \$I_f\$ of 20mA. If you're not familiar with driving LEDs (forward voltage and forward current) you should look at some of the other questions here that address how to power LEDs properly.
With these values, we can select the value of current limiting resistor using Ohm's Law: \$R = E / I\$.
$$R = \frac{3 - 2.2}{0.020} = \frac{0.8}{0.020} = 40\Omega$$
If you only plan on having one color lit at a time, you can use one resistor on the common pin:
You can use a DPDT (double pole, double throw) switch to change the direction on the motor with no other components:
However, you can't add a bipolar LED easily because it doesn't change color based on polarity, but rather on which cathode (or anode) is connected rather than open.
You could add two separate LEDs in reverse bias to each other easily like this:
To add the bipolar LED, you'll need a 3PDT switch so you can use the third pole to alternate the cathode (or anode) of the LED:
Now, none of this may actually be what you are using or how you intend to do it, but hopefully it gives you something to work from, and shows you the importance of diagrams and schematics. Good luck in your project!
Edit:
As @Wouter pointed out in the comments, you can do this with a DPDT switch:
Yep sounds like it's fried. If you are new to electronics replacing the AtMega might be difficult as it is an SMD soldered part. You would also need to load the Arduino boot loader on a new chip and that is something that requires a programmer.
I would suggest just getting a new Arduino and coming back to fix this one once you feel comfortable to troubleshoot the problem. That is a cheaper option compared to buying a programmer and parts you may need to fix this.
Best Answer
Solder won't bridge that gasp by itself - you'll need to solder a short bit of wire over the gap.
You will need to scrape some of the green solder mask off the undamaged portion of the track so you can solder to it.