You've done a good job troubleshooting your HDMI issue. The Ubuntu Live CD test confirms the issue is likely caused by hardware rather than Windows software.
To complete your troubleshooting, you want to confirm it's not an HDMI cable or HDTV issue.
1) Did your laptop successfully connect to the HDTV using your current HDMI cable before the repair?
2) Can you successfully attach a different computer to your HDTV using the current HDMI cable? OR successfully attach your laptop by using a different cable? It could also be worthwhile to see if you can reproduce the issue on a different HDTV.
3) You could try resetting the BIOS to default settings or upgrading (or downgrading) your BIOS. I've read of some strange BIOS issues in other threads.
If you choose to update your BIOS, please download the BIOS file directly to a USB flash drive formatted to a single FAT32 partition, so you are not. copying the file from the NTFS file system. Use the EasyFlash utility in the BIOS to perform the BIOS update.
Be aware that any problems during a BIOS flash may render your laptop unusable.
G74SX-A1 - stock hardware - BIOS 202 - 2nd Monitor VISIO VF551XVT