Hold it open a centimeter?? That's just a bit below being fully open, the disc shouldn't even spin that far away.
Part of it may be the battery needing replacing or a full recharge. I'm thinking you may need to contact Sony on this one if that doesn't help things. Something is seriously messed up in the UMD drive.
Sorry i can't be of more help but this is the first time I have heard of this sort of thing happening.