I used to have a dv9000 and had to replace the inverter last year. They are pretty cheap and easy to do on the dv9000 series.
Do what WR2 says, that will decypher if it's inverter or LCD, since you get video on external I'm pretty sure it's not video related, but some of the dv9000 series had bad video card issues and ended up getting recalled. Might look into that just to be sure yours isn't affected.