Interesting. You can see from my scope plot that LED04 is only driven low when a switch is pressed. Note: I had to change the assignment for LED04 from P15.2 to P3.5. When it was on P15.2, I did get a stuck low condition. I thought it was because on my 059-Kit I has a 32K XTAL soldered on to P15.2. Maybe that's not it.
There are three other reasons I can think of that might be causing what you are seeing.
PS: Don't give up. You're nearly there!