I've had my laptops on 24/7 since i got them. Total time off, and that's in suspend or hibernation mode, probably total less than an entire day (just to take it to and back from work, which is a 15min drive).
Your problem with the computer being slow is probably from all the junk that you've put on it. Since you thought simply having a computer on all the time could possibly be causing your problems, i'm assuming you're not very technically oriented, and you've probably installed one too many bonzai buddies.
Most people i would suggest to run some adware scanners, virus scanner, go through add/remove and remove anything that you no longer use, clean up the registry, etc etc, but in your case, just reformat and reinstall.