When you hold down the Clear and Volume down buttons does the remote control flash at the top? This is when you would input one of the codes associated with your TV brand but the remote needs to be pointed away from the television when you do this.
If your television is turning off when the TiVo® has the power saving setting turned off, perhaps there's also a power saving setting on your TV?
Have you found all the codes for your LG television? I have added a link here which will give all the codes so if you scroll down to LG then try the codes one at a time one of those codes should pair your box with your television so you can use the mute and volume functions.