You didn’t say what happened when you plugged in an external screen thus I’d speculate nothing changed in the pattern, partial boot and then black screen. If that’s the case, then yes, you probably have a GPU issue. If you use your Mac for professional purposes and need the discrete GPU a logic board replacement would be your best option. Otherwise you may investigate disabling the GPU and just use integrated graphics, there are several alternatives available, from primitive to sophisticated solutions, Google around and you’ll get a good picture. If you go for board replacement you can manage yourself too, just take plenty of time and patience and you’ll be fine, being concerned about mistakes is usually a sufficiently good approach. Here’s a guide, just in case:
[guide|9725]