I have a laptop Lenovo G575. MS Windows works without any problems on it, but with Linux, it freezes during login or up to 10 minutes after power on. I have tried Ubuntu, Fedora 15 and 16, Fedora 16 KDE spin, Fedora 16 XFCE spin, openSUSE, Pinguy and possibly some other distro as well. XFCE power manager got SIGTRAP when XFCE session started. It works without any problem on AC cord or if battery is more than about 50-60% charged.
Edit: Fedora 16 KDE spin works a bit better, but it freezes unpredictably on login. Lower the battery, more often it happens.