Yep, that would drive me up a wall too. God damn that was unpleasant.
But, it doesn't sound like something coming from your mobo. It sounds like a squeeky fan. I base that assumption on how irregular the "beep" is. Try spraying the fan with compressed air, and if that doesn't work, open the laptop (might void warranty), find the fan, and spin it manually to see if it squeeks. Hell, I would even consider turning it on with the laptop opened up to really make sure