How do I fix my screen that goes completely black?

So, I have had this model (Processor - 2.13 GHz Intel Core 2 Duo, Memory - 2 GB 800 MHz DDR2 SDRAM) for six years.

I'm running Mavericks and started noticing that when I adjust the screen past 30% brightness, it goes black. What I mean by this, is I can barely see the what's on the screen, without any backlight (if I hold it up to a light source I can see what the screen is displaying). I have been told that this model does not have an inverter, so I am wondering what I would be replacing. I have a brand new battery from Apple (which didn't help the issue at all).

One thing I noticed when unplugged (not charging) is if I start the screen at a 90 degree angle between the keyboard and the screen, I can keep my screen at 100% brightness. If I go to close my laptop, decreasing that angle, I can still keep my screen at 100% brightness. It is only when I go from decreasing that angle to opening it back up (from 20 degrees to 65 degrees), that the screen will go black. Once the angle between the screen and keyboard is greater than 90, I can go back and forth, without the screen going black.