Display problem

Doesn't make sense that you can't move the card , did you move the plastic latch that hlods pci-e cards in the slot? What do you mean by tried external display? Your desciption sounds like either the monitor or the video card is defective, Are you still able to under warrenty call Dell support?

Wait did you try a different monitor- I can't tell from your post. If the problem does lie in your graphics card, then you either will need to get a different one (make sure you have enough wattage for the new one) or worst case scenario a new graphics card and motherboard. It's impossible to know exactly what the problem is without some more troubleshooting on your part but we can deduce a few components that should be running fine.

1. RAM (if this was not the case you would probably get a weird error message)
2. CPU
3. HDD

Another possibility could be the power supply. How old is this computer and is it under warranty? If it's under warranty, just send it back and save yourself the trouble.

It being a laptop, a new GPU isn't possible.

The fault is caused by the monitor not syncing with the graphics card, this could be caused by the sync rate being wrong (faulty graphics card) or broken connection from the graphics card to the monitor (cable not plugged in properly or cable broken) or a faulty monitor.
The on-board graphics will be disabled when the graphics card is fitted which is why it was black when you plugged the cable into it. The graphics card is held into place by a little latch at the bottom end of the graphics card and a screw at the top front end. Graphics cards are not glued into place.

Sounds like a connection issue with the ribbon connector