I've fixed a few TV's/PVR's for friends and family. It's almost always the power supplies that pack in - usually the diodes in the switch modes PSU's. Things with external power bricks aren't worth fixing - just replace the brick. But TV's more often have a built in mains switch mode supply
IMV turning small electrical/electronic devices on and off to save electricity is false economy. Turning stuff on is usually when the PSU's have the greatest loads put on them, as they charge all the internal smoothing capacitors. This strain is when the PSU is most likely to fail. Once the TV is up and running the load on the PSU is fairly constant - there are fewer surge loads. I can't remember the last time something went 'pop' whilst it was in normal use. I can remember lots of things that went 'pop' as I tried to turn them on.
I haven't checked what my setup draws (Humax Freeview PVR + generic 42" flat screen telly), but I doubt it's anything like 20W. Even if it is, running a 20W load for 24 hours costs about 9.5 pence - so less than £35 a year. I think my PVR box was around £100, and the TV about £300. I doubt either would last more than a few years if they were turned on and off 365 times per year.
So £35 for ever, or £300+ every few years to replace the TV because some fool has been turning it on and off every night to "save money". Hmmm.