A bad power supply, broken power cord, failed on/off switch or bad drive motor can prevent the band saw from starting. Check the power supply first. Plug a shop light or other electrical tool into the electrical outlet that you're using for the band saw to make sure the outlet works. If the electrical outlet is dead, reset the house circuit breaker for the outlet. If the outlet still doesn't work, try using a different outlet to power the band saw.
If the electrical outlet is okay, unplug the band saw and check the power cord for damage. Replace the cord if it's damaged. If the power cord is okay, use a multimeter to check for continuity through the on/off switch with the switch turned on (with the band saw still unplugged). The meter should measure near 0 ohms of resistance through the switch. If the meter measures infinite resistance, replace the switch because it's preventing the drive motor from getting power.
If the on/off switch is okay, check the wire harness connections between the switch and the drive motor. Reconnect any loose wires and repair any broken wires. If the wiring connections are okay, then you'll likely need to replace the drive motor because it doesn't run even though it should be getting electrical current through the power cord, on/off switch and wires.