Shpitz,
I'm just offering some humble advice here, but speaking from (bad) experience, I think this is a case of your ps 2 being in the wrong mode.
I'm not sure, but I think no matter what chip you've installed, you need to switch between ps 1 and ps 2 modes to play the respective formats.
Try switching modes, and see it the ps 2 disks will play.
I encountered a similar problem when I first bought my ps 2, too, where the ps 1 games would not start, and only the ps 2 ones would load. I later discovered I was just trying to boot the disks in the wrong format mode.
Then again, you DID say they actually booted, even if rarely so, which means it could be a completely different problem. No harm trying, though
Hope this help!