One of my stock Amiga 2000 does the same i have to boot a few times before it works. I found a place on the motherboard that when i push there, it works otherwise i can boot up 10 times before it work. It is very strange, but when i push there it always seem to work, but then i am forced to have it open a lot.
This is almost always caused by bad chip to socket contact,a socket with a broken internal pin,and/or corroded chips and socket pins. you can pull each chip and check it and the sockets.lightly sand the chip pins with a piece of 600grit paper (very lightly!) and reinstall the chips. If that doesn't cure it suspect a socket.
