First the display:
Since you have external video, its unlikely to be a fault on the logic board. The other common logic fault which manifests on the screen causes the inverter to stop working, so you get no backlight.
The extra two pin (blue and white cable) connector you mention is for the sleep LED. Nothing to do with display. Its just data and backlight (inverter is in the bottom half).
It might be worth chatting up your local Apple engineer to see if you can get them to run Mac Test Pro on it and test the board. If it doesn't fail, its not necessarliy fine, but if it does at least you'll know what the problem is.
Is the display detected in the System Profile? If not, its either the display or the cable. It should report a model and make. Usually Samsung, Sharp, or LG/Philips As I recall.
You say you got a replacement display on eBay. Do you mean display cable? Or did you swap out the LCD too? If you did, it would seem to point at the logic board, but this still feels like a data cable issue. Its possible you have another bad cable or display (whichever it was you bought). I have seen data cables fall out of their sockets at the LCD end due to dropping. Not on Titaniums, but I assume whichever part you swapped you checked this out?
As for your other issues, the disc burning one sounds like a software issue that should be fixed by an archive & install, but the HD not showing up over target mode sounds like another problem. Either the HD is on its way out, or again the logic board may be faulty. Does target mode show up in Disk Utility or system profile on the host Mac? If it says Target mode under the firewire bus on system profile, the logic board is probably OK, and the HD is dying or very corrupt.
If that external burner was firewire, maybe you have blown your firewire controller (If System Profile reports no info available, its not seeing the bus at all, and its probably blown). Or was this one reading discs OK too?