It also uses power when it is off, but significantly less.
I have figured that my main PC uses about $80 worth of power per year, my older server uses right around $100 per year. They are both on 24/7.
One thing you can do to help lower power consumption is to turn on the Hard Disk spindown feature under power options. It will save a good chunk of power. Also set your monitor to turn off after like 10 min or so.
For me though frankly $80 a year is not much, and I have a pretty large/performance rig.
$80 is only around $6.50 a month on the bill...not much when you take into account that my bill is about $300 a month
My power bill went up $15 when I built my new rig that was always left on due to an Asus bios issue with suspend. Now that the computer can do S3 suspend and not crash I use it all the time when not on the computer, my power bill dropped back down to what it was before.
My killawatt says my rig comp+monitor eats ~500w of power idle but on, my monitor is about 200w of that, under full load the usage for the comp jumps into the 650w range, in S3 mode it eats 30-40w, 20w of that being the monitor.
My computer is in my bedroom, the first month it was on my room temp went up 5*f according to the inside/outside temp thingy on my window, now it is back down to what it was before.
I would suggest just giving your folks a bit of money each month; the PC does use power, and it will show them that you're willing to take responsibility for your toys