Q: MacBook screen goes black when opened

Depending on the exact build model series 13-inch MacBook (circa 2006 to 2010)

the specifications and internal structure of the computer main base section varies.

Your identification of MacBook, as 13-inch, Early 2009 implies it is white poly case.

(If the unit is an aluminum bodied 13-inch 'non-pro' model it would be a Late 2008.)

Introduced    January 2009

Discontinued    May 2009

Model Identifier    MacBook5,2

Model Number    A1181

EMC    2300

Order Number    MB881LL/A

There are components inside the base/keyboard area and behind the display, that

can show defects when the top is hinged open beyond a certain degree; for a time

that can still work OK but then those worn components can fail completely...

Distinguishing between inverter problem and LCD cable problem - ifixit

The iFixit guides from the approximate time-line could be helpful in determining the

parts involved, their correct identity by name + number, and replacement cost.

Inverter, inverter cable, and a few other parts come to mind as suspect as they fail.

Also there is a data cable shown in the iFixit guide page; see main for other guides.

{My first-edition 13-inch MacBook1.1 with 1.83GHz coreduo, does the same thing.}

A look through the iFixit guides site, shows this to be a likely guide for white early 2009

https://www.ifixit.com/Device/MacBook_Core_2_Duo

Sources of replacement parts can include places such as powerbookmedic.com,

ifixit.com, and others; some repair services can fix logic boards & test entire mac...

Some at a distance can entice with a full service shop, better price, & reputation.

Anyway, hopefully the parts and guide can help you decide.

You can get a repaired MacBook 13-inch model, sometimes for the cost of a repair;

I've looked into wegenermedia.com online (they repair) and occasionally see a few.

Good luck!