A Factory Restore (with nothing else installed) should've resolved the issue if it was a software problem.
The test with an external HDTV cannot distinguish between a problem cable, cable connection, or faulty display. However, I believe the odds favor a problem cable connection, followed by a faulty cable. If you're comfortable disassembling the laptop, you might check that out. Otherwise, you may need to have someone repair your laptop.
It still may be useful to check CPU and GPU temperatures to eliminate the less likely possibility that overheating is causing this issue.
G74SX-A1 - stock hardware - BIOS 202 - 2nd Monitor VISIO VF551XVT