I leave my computer on 24/7. The trading computer acts as a server. There is no reason to turn it off since I run my trading software all day and night. I have an automated trading strategy that needs to run all the time to get the full effects while trading the Forex market. I will reboot the computer once a day just to get a fresh session. I notice that the computer slows down over the course of the day so this is the reason for the reboot. By the way, I have 4 computers running all day and night. It keeps one of the bedrooms nice and toasty during the winter.
Whenever you need to think about something you should turn the computer off and let the gray matter between your ears take over.
annual cost of electricty assuming 13 cents per kwh: leaving your computer on only when you need it (assuming 5 hrs per day): $59 leaving your computer on 24/7: $284 and that's just for the computer (not monitor). if you dislike the startup time, just hibernate/standby. i've been doing that for years.