Your rig probably consumes between 300-700 watts while idle I'm guessing. Probably less if it's not a gaming pc.

here in the US, cost per kwh ranges from 5 to 17 cents. So all night, 8 hours will cost you between 2.4 and 5.6 kwh so 12 cents to 95.2

I highly doubt you'll be using 700 watts while IDLE though, unless you have triple sli gtx 470's. :/ So worst case scenario, it's 1 buck max. Average, probably just 25-50 cents. It's not too bad.

Judging from your low ram amount, i'm assuming it's not a gaming rig, so probably much less, maybe 150-200 watts. So likely, no more than 25 cents of power consumed overnight. You'll be fine, don't worry :P

As for slowing down, installing the game shouldn't cause any drastic change in startup. Did it install any update services and stuff though? Or maybe it installed steam? Maybe one program it installed was enough to push your pc to the limit.

Also, hate to say this, but for "downloaded" "not legal"
VIRUS. You didn't seem to notice this the first time on page one so i'll resort to blinding text (apologies)