My first thought is your USB interface chip (FT232RL) is short-circuiting the power supply, and that's causing the polymeric fuse to open, then cool down and work again, then open, then cool down, etc.
With two identical Megas, one of which isn't recognized as a USB device, that's pretty strong evidence for a broken USB interface chip. Now, by "doesn't establish a USB connection" do you mean that it doesn't even show up on your computer? (that's what I've been assuming)
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