Vacuum cleaners are offered in many different shapes and sizes and at different price points, but like nearly anything mechanical, sometimes something goes awry that results in the machine's failure to turn on. In this happens, a few troubleshooting tips may negate the need to have the cleaner serviced or replaced.
Make sure the vacuum is plugged in all the way into the power source. Some outlets have loose receptacles that prevent the plug's prongs from making full contact, so try plugging the vacuum's cord into different wall outlets in your home or apartment. Turn the vacuum on. If a loose outlet's to blame, run an extension cord from another outlet to the vacuum until you can address the outlet later.
Empty the canister or bag on your vacuum cleaner. In some models, particularly newer models from the last decade or so, a full canister will prevent the vacuum from being turned on. This is done as a precaution to prevent further use of the cleaner and potential straining of the motor.
Inspect the vacuum cleaner cord, especially the point of attachment where the cord meets the vacuum. Check for any splits or splices in the rubber covering that may expose the wiring underneath or check to make sure the cord isn't loose in the connection to the cleaner. Wrap a generous amount of electrical tape over small splits in the cord; for loose connections, contact a repair technician, as you'll probably have to replace the cord.