Since most of our industries use induction motors, it is essential to develop condition monitoring systems. Nowadays, industries have power quality issues such as sag, swell, harmonics, and transients. Thus, a condition monitoring system should have the ability to detect various faults, even in the presence of power quality issues. Most of the fault diagnosis and condition monitoring methods proposed earlier misidentified the faults and caused the condition monitoring system to fail because of misclassification due to power quality. The proposed method uses power quality data along with starting current data to identify the broken rotor bar and bearing fault in induction motors. The discrete wavelet transform (DWT) is used to decompose the current waveform, and then different features such as mean, standard deviation, entropy, and norm are calculated. The neural network (NN) classifier is used for classifying the faults and for analyzing the classification accuracy for various cases. The classification accuracy is 96.7% while considering power quality issues, whereas in a typical case, it is 93.3%. The proposed methodology is suitable for hardware implementation, which merges mean, standard deviation, entropy, and norm with the consideration of power quality issues, and the trained NN proves stable in the detection of the rotor and bearing faults.