Did anyone manage to figure out the no PS2/black screen issue? I recently bought a frankie CECHA00 done by Sony and it had some problems with playing PS2 games. I've "solved" it by having the fan use SYSCON settings when starting a PS2 game, and while playing, it can ramp up as much as it wants...
Just wanted to add my experience with this issue.
I recently bought a frankie CECHA00 from Japan done by Sony themselves. The seller I got it from also claims to have delided the CPU and replaced the paste on both the CELL and RSX. I say "claimed" because I haven't opened the console myself...