MacBook Pro 3.1 internal (replacement) LCD not detected by graphics card; external monitor OK

Solution: Buy a new Display, the old one seems to be broken

I tested my laptop with another display and there weren't any problems with other displays so my conclusion was that the display has to be the error (the display is old and used up).

NOTE: Sorry that I didn't answer my own question, I forgot about it.

You might try attaching the second monitor and running Apple Hardware Test upon boot.

To run the hardware test:

1. Print these instructions for reference
2. Disconnect all external devices except the keyboard, mouse, display, and speakers. If you have an Ethernet cable or external DVD drive, disconnect it.
3. Restart your Mac, holding down the D key while the Mac restarts.

4. After your Mac restarts, you should see the Apple Hardware Test chooser screen. If you don’t, Apple Hardware Test may not be available on your Mac. You may be able to start Apple Hardware Test from the Internet. Reconnect your Mac to the network, then restart your Mac while holding down both the Option and D keys.

5. When the Apple Hardware Test chooser screen appears, select the language you want to use, then press the Return key or click the right arrow button.

6. When the Apple Hardware Test main screen appears (after about 45 seconds), follow the onscreen instructions.

If you can't see anything on your secondary display after starting Apple Hardware Test, then it may have started but not recognized your secondary display. You could press Enter and then T to start the tests, but there's probably no way to see the results. If this is the case, you're probably better off taking it to the Apple Store. It sounds like the LCD is faulty.

Here is a list of other startup keyboard shortcuts.

LCDTest

You might try running this LCDTest program to check whether any RBG test patterns show up or change the display output. If you still don't see any output, and you've checked that the LCD Display shows up under System Preferences => Displays, then you may have a hardware problem with your Display Data Connector, or LCD Display.

LCD Hardware Problem

This is most likely a hardware problem, and taking it in to the Apple Store for support is probably your best bet if it's still under warranty. You can check if your Macbook's warranty is still active by visiting this page and entering your serial number.

If it's out of warranty, or you really want to try and solve this yourself (this will void your warranty), then dive into the iFixIt Guide for Replacing a MacBook Pro 13" Mid 2009 Display. iFixIt sells Replacement Parts for your Macbook.