This problem is commonly encountered because the game doesn't support the LED's. First, check to make sure whether or not the game supports the shift lights. If it doesn't work, there is 3rd party software to force the LED's to work. If the game supports the lights, check to make sure the LED's are enabled in the Logitech Profiler. If none of these solutions work, it is most likely a hardware problem. To fix this, you will have to either replace the LED's or fix their connections. For either of these fixes, check out the troubleshooting page.
This could be a problem within the settings of the game or the Logitech Profiler. Make sure that force feedback is enabled in game and checked in Logitech Profiler. If this doesn't work, the wheel could have a looses connection to the computer or console, or the A/C power adapter is unplugged or not functioning. To fix this, unplug and re-plug in each connection to the wheel and computer. Also, restart the Logitech Profiler, the game, and the wheel. If none of this works, check the troubleshooting page for other potential fixes. Hope this helps. Logitech G27 Troubleshooting