Lack of electrical power, a failed electronic control board, faulty user interface control, failed fan or light switches, a bad fan motor or bad light sockets can prevent the range hood from working at all.
Check the house circuit breaker and reset if tripped. If the house circuit breaker didn't trip, check the range hood's electrical outlet for power by plugging a small appliance or lamp into the outlet to see if the outlet works. If the outlet works, leave the range hood's power cord unplugged and check the power cord wiring to the range hood control. Reconnect loose power cord wires or replace the power cord if it's damaged.
With the power cord still unplugged, check the electronic control board for burn marks that indicate a control board failure. Replace the control board if you find burn marks on the circuit board. If your range hood uses a user interface control to start the fan and control the lights, you may need to replace the user interface if it isn't sending signals to the electronic control board when you press user interface buttons. A user interface control is a keypad and display panel that sends signals to the electronic control board through a ribbon wire cable when you press its selection buttons. DIY testing of the user interface control isn't available for most range hood models so you can't tell whether a failed electronic control board or a failed user interface control is preventing the range hood from working. If the electronic control board doesn't respond when you press the power button, you'll likely need to replace the electronic control. If the range hood still doesn't power up after replacing the electronic control board, you'll likely need to replace the user interface control.
If your range hood uses switches for the fan and lights, disconnect power and check continuity through the switches using a multimeter to see if the switches allow current to flow to the lights and fan motor when you turn on the switches. Replace the switches if you don't measure continuity through the switches when they're turned on.
If the fan switch or the electronic control board sends electric current to the fan motor but the motor doesn't run, replace the fan motor. If the light switch or electronic control board sends current to the lights but the lights don't work and you already replaced the bulbs, replace the light sockets.