Remote dead Do not work anymore

Sounds like the contacts in the buttons are not making contact.. you may want to try taking the remote apart and cleaning the contacts and seeing what happens. If the remote is truely dead you may need a new remote

Check it for its infrared emission. Check it with fresh batteries. Clean the battery contacts inside the battery compartment, before inserting batteries to make sure that the batteries are in good contact.To get more details, http://electronicshelponline.blogspot.com/ Pull up older posts. It has details about how to check a remote control.

have to replace the failed battery

You usually don't have to sync it. Simply remove the batteries and replug them. If it still doesn't work, they might be dead.

If the status light no longer illuminates when pressing the remote (where it did before), the most common reason is a dead battery. If, after changing the battery, the light still fails to illuminate, the problem may be corrosion on the contact points for the battery or, the buttons are not making contact on the circuit board.

ok i know this might sound wiered but i just had the samething happen what i did was i cleaned the key with soap and water dryed off , locked the door with key and unlocked with key then got in jeep tryed starting it ,it started right up gauges all work now and windows work and running fine doesnt shut anymore.

try to change the battery in the button mite be to dead t ostart but not dead to unlock doors.

If you have the Vehicle Owners Manual it will instruct you how to reset the Electronic Remote(s) as disconnecting the Battery or a totally discharged battery removes all power from the On Board Chassis Computers memory. Therefore you must reset the Remote(s) so that the On Board Chassis Computer can recognize them. If in Doubt, please consult your Chevrolet Dealer to rectify the problem.

They fail more often than the appliance they control because they are often dropped etc.
Here is how to repair your remote:
http://www.google.co.nz/url?sa=t&source=web&ct=res&cd=1&url=http%3A%2F%2Fwww.instructables.com%2Fid%2FRepair-your-remote-controls%2F&ei=mpVVSrr6O4_-sgP0-oDPDg&usg=AFQjCNGyomjVuVMr6mFT1L36ffi06FhCDg&sig2=kheNi9TulBWzmhGOMiIX7g