How to Detect if Motor is not Working?
You are not thinking this through. Using your circuit configuration







simulate this circuit &ndash; Schematic created using CircuitLab

Start by assuming the motor is drawing 3 A, and the relay coil is drawing 150 mA. Then the transistor collector current is also drawing 150 mA. Because the transistor should be acting as a switch, its base current should be in the range of 1/10 to 1/20 the collector current, or about 10 mA. Then the voltage across RSENSE should be $$V_{RSENSE} = 0.7 + I_b \times RBASE$$ For a 47 ohm RBASE, this works out to $$V_{RSENSE} = 0.7 + .01 \times 47 = 0.7 + .47 = 1.17\text{ volts}$$ and the power dissipated in RSENSE $$P = i VSENSE= 3\times1.17 = 3.5\text{ watts}$$ so you'll need RSENSE to be at least 3.5 watts, and a 5-watt resistor would be a reasonable choice. 

Note that, whatever you do, RSENSE will need to dissipate a lot of power. This is because the voltage across RSENSE must be higher than the 0.7 volts needed to turn on the transistor. Operating with no safety margin, such a 0.7 volts at 3 amps will dissipate 3 times 0.7, or 2.1 watts. This would require a 0 ohm base resistor, and this would not remotely be a good idea. In your edited circuit, the reason it's not working is that RSENSE is only providing about 0.6 volts, and needs to be about 0.4 ohms in order to develop enough voltage across RBASE to drive the transistor (you can do this quickly by adding another 0.2 ohm resistor in series). Note that both resistors should be at least 2 watt units.