If you can run an external display, that means you likely do not have the dreaded and well-documented Nvidea 8600 failure (I lost my 2007 MBP to it last June). Were it the 8600 problem, an external display would not work.
Likely causes for your problem are :
<>broken video cable where it goes through the hinge
<>failed backlight on the built-in display
These are fixable for much less that the complete logic board replacement the the Nvdea 8600 failure requires.
The Nvidea 8600 repair extension program expired just over a year ago:
At this point, you have basically diagnosed the issues as far as you can by determining what does and doesn't happen on the external display. If you have your original system disks, one has Apple Hardware Test (AHT). That might pick up a failed inverter but I doubt it picks up a failed backlight or a broken cable.
I don't know if you can run AHT with an external monitor. The test boots from the DVD so you may not have extensions needed to fire up the external. You can try--just make sure your external is set to "mirrored mode," not "extended desktop," before restarting from the DVD and you have a chance of it working.
AHT will give you a cryptic code if something fails; post the code and I can try to translate.
If AHT doesn't further narrow the suspects, you'll need to have it looked at by a pro to get anywhere, unless you are comfortable taking apart something loaded with tiny and delicate electronic bits. If so, tell me your screen size and I can point you to some illustrated maintenance sites.