Ive never heard of an app have the capability of causing such things, malicious or not. Did you flash something that you shouldn't have? What you are describing sounds more like a bad flash more than a rogue app. Otherwise I would be more inclined to think that you have a hardware problem. If you havent already, remove your sd card if you have one, and hold the power button for a minimum of 20 seconds and see if it turns on. If not, try charging your note for 24 hours even if it doesn't display charging information. Then try turning it on normally. If not, hold the power for 20 seconds. After that, I would say that you would need to contact Samsung for warranty repair or exchange.
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Samsung Galaxy SIII SGH-I747
CyanogenMod v10.2 | Android v4.3.1
CWM Recovery v184.108.40.206
Samsung Galaxy Note 8 GT-5110
CivZ FlexBeam Rev3.6.1 | Android v4.2.2
CWM Recovery v220.127.116.11 Touch by CivZ