I don't think the inverter would have anything to do with the grey lines. It's job is to change the low voltage (12V DC) in your laptop to high voltage (?V AC) in order to drive the light tubes in the back of the screen.
A good quality inverter might deliver a better, more stable, higher current voltage to the tubes, possibly making them brighter (or possibly damaging them if voltage/current overdriven).
Sorry I don't know where you could get a replacement for the inverter.
The grey lines might be casesd by two factors: 1. mechanical problem during the panel assembly where the screen layers don't line up perfectly. 2. Wrong horizontal or vertical sync frequency making the screen appear washed out.
I don't think the original screen is machanically damaged in some way. It's a good quality screen made by a good LCD company - Samsung. I just read another post that said that upgrading to bios 3311 increases brightness of the screen and get's rid of grey lines. Well, I can test the brightness, but my grey lines are gone by now
I'll see if I can post the step by step on the screen replacement with some pics.