37 inch LG LCD 720p
If everything else on the remote works, most likely the PWR function on the remote is not working.
This may be a problem with the conductive rubber membrane under the button, or the matracy circuit is not reading the function due to any number of problems.
You can call the manufacture parts rep to see if it is possible to have parts for the remote. Most of the time, they are not worth to service, and parts are not sold to support remote control service. You will most likely have to order a new remote from the manufacture rep.
I suggest to NOT buy a universal remote. They rarely can do more than the most basic functions. Many times universal remotes have different issues with different models of sets.