Ok then, I don't know if a higher wattage will help with it as I'm no expert but it may. Try getting a better quality one as well - not saying your's wasn't good quality but it's a good idea to get a better quality one in case. Also see if there's a warranty in case you have problems in the future with it.
I don't know if it will just plug in and work, mine did when I repaired my old PC it's running 24/7 and restarts two times a day.