Well, the first PS2 sounds like either the mainboard fuse has either blown around the BA chip, or the BA chip itself has gone - or maybe both.
The second sounds like either the laser has died, or chances are a quick calibration would fix it up. Try ShadowKnyghts website here, it has a very good laser calibration guide:
http://www.cyber-mag.com/station/ps2tips.htm
Either way, I can help you out on MSN. I'll have to catch you either this afternoon or tomorrow some time, as it's my 18th tonight and I'm getting ratted
