Check the motion sensor functionality by holding the Wii Remote with the button side down. Without using much force, tap the button side of the remote against the palm of your other hand. Doing this does not take a lot of force, so be sure not to tap the Wii Remote very hard.
When you turn the remote on, do the lights flash and then turn off, or not turn on at all? Also, does the cursor appear on the screen at all, even if it is momentary or erratic?
If other Wii remotes do work, and this is the only remote that has a problem, then I'm afraid that it is broken. Unless you have something like a remote cover obscuring the remote's tip, you will need to get another remote.
If other Wii remotes do not work, check the sensor bar with these instructions.
If the lights are not working on the sensor bar, check if the sensor bar is plugged in properly. If it is, and the lights are still not working, then you can call nintendo and talk to them about it. I did and they gave me a free sensor bar because mine wasnt working. I think they only give you a free sensor bar if your wii still has a warrenty though. If not, you can go onto nintendos online store and buy a sensor bar. Click this link to buy a sensor bar: http://store.nintendo.com/webapp/wcs/stores/servlet/ProductDisplay?productId=138704¤cy=CAD&catalogId=10001&tranId=0&lastAction=setCurr&storeId=10001&languageId=-1&categoryId=62716&ddkey=http:SetCurrencyPreference
The new sensor bar will cost about $10.00.
Hope this helps!