Erm, let me think here.
You have an A10-5700 with so a cpu and a Gpu.
What is the default monitor set to, and the default screen setup in catalyst control center ?
If you have a monitor i would hook it up to that, if it works then some tweaking may have to be done in ccc, before connecting it to the tv. Also I would check out if you have to set the refresh rate to the right frequency, it will depend on how the tv does HD at 1080p or 1080I interlaced mode. it may need to be changed.