I have an older (7years) Soyo model DYLT3212 flat screen. I am trying to hook Amazon FireTV up to via an hdmi cable. The Soyo has no hdmi input. Facing down on the back of the TV appears to be both

SOURCE: soyo dylto32c

The DVI input on this set is meant for picture only.. ex. to display computer picture.
if you want audio with your picture. you must connect to either inputs YCBCr or YPbPr which both of those inputs has audio inputs.

SOURCE: how do i connect a dvd player to soyo atlas dylt3212 32in

you have to use the remote and hit the input button , look at the back of the tv where you plugged the cables in, it will tell you what input it is plugged into, chang your input to that one on the tv- using the input button

SOURCE: where do I get a cable to connect my laptop pc to

You will need either a DVI-I to DVI-I cable or a DVI-I to HDMI cable. Your computer should have a DVI-I output or HDMI. You can not directly connect a VGA output to the TV. If needed, you can purchase a VGA to component (Y/Pb/Pr) converter.