For my high school physics class we have been assigned a project where we must solder and assemble a circuit, so we picked an Escape Robot Kit. We soldered and assemble and it won't work at all. There must be a problem with how we soldered or something. Any ideas of how to potentially quickly solve the situation?
It will take as long as it takes.
Find a DVM and measure every voltage on the circuit with respect to ground (or -ve supply). Pencil them in on the circuit. Then sit down and consider how the circuit works and see if the voltages stack up. If you have a wrong voltage, look around that stage for an error. Work your way back towards the input until the voltages are correct.
Assume that the design and circuit are correct. Don't attempt to modify the design. Just look for errors on your part. Don't discount faulty components. Quite often new, out of the box components can be faulty.