I have a LG Xcanvas TV and a satellite decoder(the Multichoice satellite decoder), while the TV is switched on the decoder remote mulfunctions and hardly works(it's as if the batteries are flat). Turn the TV off and the decoder remote works perfectly.

Double check on the remote, that you have it in SAT mode instead of TV mode. There should either be a mode button or just buttons labeled things like "TV" and "SAT".

If that doesn't work, then it may be the "programming" of the remote.

No option to select a different mode. The decoder is a Multichoice DSD 1110. The remote worked perfectly with another TV(Haier) that I had, but now I have a LG Xcanvas HD and the remote works intermittingly.

I recently discussed this. It's due to the TV intensity interfering with the remote. The fix is an LCD/plasma compatible IR repearer system. See Xantech.com